182 Chapter 8. Discussion Among the modelling choices when implementing Markov chains to model deterioration in sewer mains is the assumption that time transitions are either homogeneous or inhomogeneous. Both approaches are used in the literature (see Table II.3, page 107). Homogeneous-time Markov chains are simpler due to their constant transition rate, but our results indicate that inhomogeneous-time Markov chains better capture non-linear stochastic behaviours. However, this adds degrees of freedom, sometimes leading to overfitting. Future work should focus on more robust calibration methods to enhance predictability. Properly calibrated, inhomogeneous models should capture homogeneous behaviours, but not vice versa. As pointed out before, the inspection data in sewer mains, due to the way data is collected, are interval-censored (Duchesne, Beardsell, Villeneuve, et al., 2013), which introduces uncertainty about the exact moment of transition between severity levels. This complicates the calibration of degradation models as it requires a more complex loss function, often overlooked. In this dissertation, we assess this issue using the non-parametric Turnbull estimator (Chapter 6) as a reference. Interestingly, despite not accounting for interval censoring during calibration, the predictions of our degradation models closely aligned with those from the Turnbull estimator in terms of the probability distribution over severity levels at di!erent pipe ages. This suggests, for this dataset, that the e!ect of interval censoring may be negligible, though further investigation is required to evaluate the extent of generalisation of this observation, as this could significantly simplify the model calibration process. What is the current usefulness of MSDMs? Having acknowledged the limitations in data and model assumptions, let’s now discuss the usefulness of MSDMs via Markov chains for sewer main degradation modelling. We believe that these models, when provided with ‘su"cient’ data, are useful to approximate the distribution of damage severities across a population of sewer mains. However, two scenarios where these models are less reliable—apart from covariates with data scarcity—are (i) predicting the condition at a pipe level and (ii) predicting the condition of a pipe beyond the observed data. The first issue may be improved by larger and richer datasets (e.g., synthetic data and data integration), and the second by implementing an e!ective calibration process, with a strong focus on improving prognostic capabilities. 8.3 Maintenance Optimisation: Maintenance optimisation of multi-state components Overview of the research problem in Part III Building on the findings from Part II, the next logical step was to apply MultiState Deterioration Models (MSDMs) to design maintenance policies for sewer
RkJQdWJsaXNoZXIy MjY0ODMw