6 6.3. Experimental setup and evaluation 131 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 pk (t) p k (t) p k (t) (c) Cohort PMW: (b) Cohort CR: (a) Cohort CMW: 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) 0 204060800 204060800 20406080 Pipe age (t) Pipe age (t) Pipe age (t) TE (training set) TE (test set) Log-Normal Log-Logistic Weibull Gompertz Exponential DTMC Figure 6.2: State probability p (t) k for di!erent Markov chains. Dashed lines are the Turnbull estimators. For Cohort (a) CMW, (b) CS, (c) PMW. are randomly selected for model calibration, while the remaining 30% is used to compute goodness-of-fit metrics described in Section 6.2.4. 6.3.3 Results The di!erent types of Markov chains are calibrated using data from cohorts CMW, CS, and PMW on infiltration, following the procedure described in Section 6.2.2 with the training set. Table 6.1 presents the goodness-of-fit metrics for both the training and test sets, while Figure 6.2 illustrates the state probabilities. The results from the Turnbull estimator for both sets are also displayed. The vertical grey dashed lines in the figures denote the last inspection used for model training. By solving Eq. 4.2 (page 98), we obtain the transition probability matrix over time pij(t, ϱ). Figure 6.3 displays these probabilities for cohort CS and infiltration.
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