Pipe failure modelling for water distribution networks using boosted decision trees

Figures & data

Figure 1. (left) visualises an example predictor space with observations of two classes (blue circle and green square). (1) provides two possible separations of the predictor space. (2) chooses the better classification and applies another separation on the subspaces.

Table 1. Timetable for pipe materials that changed their deterioration patterns due to different manufacturing processes as classified by Roscher (2000).

Material	Interval boundaries in years
CI	1900	1930	1970
DI	1950	1980	2000
ST	1900	1940	1980	2000
PE	1950	1975	1995

Table 2. Feature vector x of the data-set with the abbreviations used in the results. The type indicates if the feature is categorical (C) or numerical (N).

	Name	Type	Description
	Failure	C	Indicating pipe failure or not (y)
physical	Age	N	The age in years
	Type	C	The type of the pipe, classified as DP (distribution pipe), HC (house connection) and HY (hydrant pipe)
	Diameter	N	The diameter in millimetres
	Pressure	N	The nominal pressure in bar
	Length	N	The length of the pipe in metres
	Material	C	The material of the pipe section, categorised as described in Table 1
geographically derived	HC_Str	N	Number of house connections in the same street section
	HY_Str	N	The number of hydrants in the same street section
	Valves_Tot	N	The number of valves on the pipe
	Valves_St	N	The number of valves in the same street section
historically derived	Failure_Tot	N	The number of total damages recorded on the pipe
	Failure_New	N	The number damages recorded since the pipe has been replaced. If the pipe has never been replaced it coincides with Failure_Tot

Figure 2. Histograms of the pipe network data. Material appendices 1G, 2G and 3G indicate the sub-classification of materials according to Table 1. The material abbreviations denote asbestos cement (AC), cast iron (CI), ductile iron (DI), glass reinforced plastic (GRP), high impact polypropylene (HIT), polyethylene (PE), polyvinyl chloride (PVC), lead (Pb) and steel (ST). The type abbreviations denote distribution pipe (DP), house connection (HC) and hydrant (HY).

Table 3. Confusion matrices for the evaluated methods showing rates in per cent. RUSBoost is significantly different from the other methods by having a lower true positive rate and a significantly lower false positive rate.

		predicted				predicted
RUSBoost		Yes	No	Random Forest		Yes	No
actual	Yes	70.19	29.81	actual	Yes	80.62	19.38
	No	1.17	98.93		No	9.32	90.68
		predicted				predicted
AdaBoost		Yes	No	Decision Tree		Yes	No
actual	Yes	80.75	19.25	actual	Yes	79.14	20.86
	No	10.10	89.90		No	16.51	83.49

Figure 3. ROC curve for failure pipes, predicted vs. actual response on test set. RUSBoost shows the best performance as it is closes to the ideal classification, a horizontal line with true positive rate 1 for all values of false positive rate. This is also reflected by the highest area under curve (AUC) value of .93.

Figure 4. Comparison of predictor importance estimation. The predictors are sorted according to the importance for the first classifier (RUSBoost).

Figure 5. Visualisation of the pipe deterioration prediction for parts of the entire network for the current condition and future in five year steps. The pipe failure probability is visualised by colour intensity. The histograms show the failure probability distribution for the entire network.

Roscher, H. (2000). Zustandsbewertung städtischer Wasserrohrleitungen zur Vorbereitung der Rehabilitation [Condition assessment of urban water distribution pipes to precede rehabilitation]. ROHRBAU-Kongress 2000 in Weimar. FITR - Forschungsinstitut für Tief- und Rohrleitungsbau Weimar e.V, Ed, Weimar, Germany.

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