6 6.6. References 135 These models are calibrated using Metropolis-Hastings and Sequential Least Squares Programming algorithms, utilising historical inspection data from a Dutch sewer network. Additionally, we employ the Turnbull estimator as a reference to account for the interval censoring in the dataset. From the dataset, we establish three cohorts and assess the fit of the Markov chains using various goodness-of-fit metrics. Our findings suggest that, despite their complexity, inhomogeneous time Markov chains more e!ectively model the non-linear stochastic behaviours observed in sewer network inspection data. In particular, the inhomogeneous time Markov chain modelled with the Gompertz distribution consistently showed good performance. This observation aligns with Mizutani and Yuan, 2023, which recommends inhomogeneous Markov chains to model time-varying transition probabilities in bridge structures. This result is crucial for sewer asset managers, as deriving maintenance policies for sewer mains requires accounting for these non-linearities in deterioration models, since di!erent assumptions may yield distinct maintenance policy implications. To maintain the severity levels within the model and to address the non-linearities in the deterioration process of sewer mains, it is key to adequately evaluate the inhomogeneous behaviours. The use of homogeneous time Markov chains is advised only if the modeller can substantiate this assumption beforehand. Future research. Future research directions include: - Addressing the omission of interval censoring during the calibration of our inhomogeneous time Markov chains, which approximate the Turnbull estimator, requires further investigation to assess the validity of neglecting interval censoring. - Expanding our models to consider pipe length and the distribution of deterioration along the sewer main, beyond focusing solely on the most severe pipe condition during inspections. - Developing models that incorporate covariates without forming cohorts to minimise cohort selection biases. - Integrating uncertainty quantification, vital for decision-making, requires studies on accurate uncertainty bound estimation. - Despite our calibration process’s e"cacy, further exploration of alternative optimisation techniques for non-linear constrained problems is needed to improve parameter inference speed, aiming to reduce over-fitting. - Future studies should also investigate the application of these models to optimise maintenance and inspection policies in sewer networks. 6.6 References Akaike, H. (1998). “Information Theory and an Extension of the Maximum Likelihood Principle”. In: Selected Papers of Hirotugu Akaike. Ed. by E. Parzen, K. Tanabe, and
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