120 Chapter 5. Deterioration Modelling of Sewer Pipes via Discrete-Time Markov Chains: A Large-Scale Case Study in the Netherlands degrade faster than those carrying stormwater, a phenomenon commonly observed in practice. When comparing DTMC types, “Multi” and “Single” chains show similar performance. The “Single” chain is easier to calibrate due to fewer parameters, making it suitable for this study. However, the “Multi” chain requires a better implementation to avoid forming absorbing intermediate states. Future work. As for future research, we identify the following directions: - We assumed that the time-to-event (i.e., from sewer main installation to condition rating) is exact, though this may be imprecise due tointerval-censoring (Duchesne, Beardsell, Villeneuve, et al., 2013), where transitions between severity levels are unknown but occur within intervals. This assumption requires careful evaluation as it may bias DTMCs. Robust approaches, such as multi-state survival models for interval-censored data (Hout, 2016), are recommended. - Regarding the DTMCs parameter inference, approaches based on Maximum Likelihood Estimation that incorporate covariates are advised, as these eliminate the need to discretise data based on time intervals and the use of cohorts, which may yield subsets insu"cient to estimate reliable statistics. 5.6 References Ana, E. and W. Bauwens (2010). “Modeling the structural deterioration of urban drainage pipes: the state-of-the-art in statistical methods”. In: Urban Water Journal 7.1, pp. 47– 59. doi: 0.1080/15730620903447597. Baik, H.-S., H. S. Jeong, and D. M. Abraham (2006). “Estimating Transition Probabilities in Markov Chain-Based Deterioration Models for Management of Wastewater Systems”. In: Journal of Water Resources Planning and Management 132.1, pp. 15–24. doi: 10.1061/(ASCE)0733-9496(2006)132:1(15). Caradot, N., M. Riechel, M. Fesneau, N. Hernandez, A. Torres, H. Sonnenberg, E. Eckert, N. Lengemann, J. Waschnewski, and P. Rouault (2018). “Practical benchmarking of statistical and machine learning models for predicting the condition of sewer pipes in Berlin, Germany”. In: Journal of Hydroinformatics 20.5, pp. 1131–1147. doi: 10.2166/ hydro.2018.217. Duchesne, S., G. Beardsell, J.-P. Villeneuve, B. Toumbou, and K. Bouchard (2013). “A survival analysis model for sewer pipe structural deterioration”. In: ComputerAided Civil and Infrastructure Engineering 28.2, pp. 146–160. doi: 10.1111/j.14678667.2012.00773.x. Egger, C., A. Scheidegger, P. Reichert, and M. Maurer (2013). “Sewer deterioration modeling with condition data lacking historical records”. In: Water Research 47.17, pp. 6762–6779. issn: 0043-1354. doi: 10.1016/j.watres.2013.09.010. Hawari, A., F. Alkadour, M. Elmasry, and T. Zayed (2020). “A state of the art review on condition assessment models developed for sewer pipelines”. In: Engineering Applications of Artificial Intelligence 93, p. 103721. doi: 10.1016/j.engappai.2020.103721. Hout, A. van den (2016). Multi-State Survival Models for Interval-Censored Data. CRC Press, pp. 1–238. isbn: 978-146656841-9. doi: 10.1201/9781315374321. Kobayashi, K., K. Kaito, and N. Lethanh (2012). “A statistical deterioration forecasting method using hidden Markov model for infrastructure management”. In: Transportation Research Part B: Methodological 46.4, pp. 544–561. doi: 10.1016/j.trb.2011.11.008.
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