190 Chapter 9. Conclusions & Recommendations incorporate requirements set by degradation models, shifting the goal from merely assessing conditions to also generating data for these models. 3. Cohort-based approach: Dividing inspection datasets into cohorts for Markov chain calibration led to challenges, often resulting in small, unrepresentative populations of sewer mains, which undermined model reliability. Future work should develop systematic methodologies or guidelines to define cohorts more appropriately for this application. The assumption of cohort homogeneity may not hold, so addressing data heterogeneity is critical. An alternative to cohort-based approaches is to develop models that directly incorporate covariates, such as pipe location, which can generate tailored degradation curves while preserving properties such as monotonicity and damage severity levels. 4. Parameter inference: The methods used for parameter inference often converged prematurely, getting trapped in local optima. Sampling-based methods were computationally expensive, and the likelihood-based loss functions may have been insu"cient to prevent overfitting and to ensure reliable predictions. Future work should explore more robust parameter inference techniques that can avoid these pitfalls. 5. Include context: “It is implicitly assumed that the conditions between inspections were identical and that all processes occurred at a constant rate over time” (Cherqui, Clemens-Meyer, Tscheikner-Gratl, et al., 2024). This assumption is unrealistic, especially for large-scale systems like sewer mains. A potential solution, as previously mentioned, is to develop or implement methods that account for covariates such as pipe location, which would enable more realistic modelling of varying conditions. 6. Uncertainty quantification: Prognostic models ideally should incorporate uncertainty bounds to reflect confidence in their predictions, which is essential for decision-making. Degradation models based on Markov chains are no exception. For this, we initially employed sampling-based methods to estimate confidence intervals, successfully applied to Discrete-Time Markov Chains (Figure 5.2, page 118). However, for Inhomogeneous-time Markov Chains, the computational cost made these methods impractical. An alternative approach could use interval Markov chains (Kozine and Utkin, 2002), where transition probabilities lie within intervals rather than being fixed values (Sproston, 2023). The key challenge here is e"ciently infer the parameters of the interval Markov chain to represent the lower and upper confidence bounds. 7. Interval-censored data: Extending the challenges mentioned in parameter inference and uncertainty quantification, an open challenge is the consideration of interval-censoring during model calibration. This aspect is inherent in the sewer network inspection dataset, as the exact transition time between severity levels is unknown. To address this, a more complex loss function is required to properly handle interval censoring; see Hout, 2016 for further details. Additional testing of this aspect is necessary across multiple case
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