Infrastructure aging risk assessment for water distribution systems

Beginning in the 1980s, a number of attempts have been made to statistically model the failure risk of water pipelines (Vanrenterghem-Raven et al. 2004; Jafar 2006; Jafar et al. 2007, 2010; Alegre et al. 2011; Alegre & Coelho 2012; Mamo 2013; Mamo et al. 2013, 2014). The development of models for the prediction of failure in the water distribution system (WDS) encounters major difficulties, mainly due to the lack of data on both the WDS and pipe breakage history (Jafar et al. 2010; Alegre & Coelho 2012). The assessment of pipe system degradation requires information on the WDS including physical, environmental, and operational parameters that have impacted the pipe failure rate (FR) during its life-cycle (Le Gat & Eisenbeis 2000; Alegre & Coelho 2012). Pipe system aging modeling has included statistical models for predicting water pipe failure using historical data, survival data analysis and stochastic models (Jafar 2006; Jafar et al. 2007, 2010; Mamo 2013; Mamo et al. 2013, 2014) such as artificial neural networks (ANN) for forecasting failure occurrence in the network.

The purpose of this research is to establish a Decision Support System (DSS) for optimizing infrastructure asset management of WDS through a statistical analysis of the WDS FR using historical data for degradation risk assessment. To support the operator's decision-making in optimizing the network rehabilitation the proposed statistical analysis method yields

• For a pre-established Failure Rate (F_R) of a cluster of pipes, defined by the pipe characteristics (i.e. year of installation, materials, diameter), the Probability (P_r(F_R)) of exceeding the selected F_R value as a function of the Age (T) of the pipes

• For an Acceptable Probability (or Risk) of exceeding a pre-selected F_R value the variation of the F_R value as a function of the Age (T) of the pipes

• An operator's experiencebased Risk Matrix to identify the risk of exceeding a pre-selected F_R value at a specific Age (T).

The proposed Risk Assessment Method (RAM) is based upon the use of both statistical and stochastic models for the network micro-zone degradation rate assessment to enable optimization and prioritization of asset management and rehabilitation works. The use of Geographical Information Systems (GIS) for the construction of the database presents a specific interest in facilitating access to information on the water network (Jafar 2006; Jafar et al. 2007, 2010; Mamo 2013; Mamo et al. 2013, 2014). For this demo-illustration the RAM application used data on pipe failures collected in the City of Wattrelos, France.

where:

• N_i/N_F is the frequency of a selected F_Ri value (or range of values)

• N_F is the total number of years for the selected time period

• i is the serial number of a selected F_Ri value in a time series of N_F values.

For a selected age (T), a risk matrix, indicating a risk level on a color-coded scale (i.e. 1 to 4, corresponding to increasing deterioration severity level), is established based upon the Failure Rate (F_Ri(T)) for the cluster of pipes under consideration and the acceptable risk P_rA of exceeding the selected F_Ri value.

• Scale parameter (or characteristic life-cycle). For a selected Age (T) the Weibull CDF of the FR is obtained by substituting t = F_Ri and using for a scale parameter F_R0 = 1 Failure per 1 km per 1 year.

• Shape parameter (or degradation rate parameter)

• Location parameter (or failure-free life-cycle), representing a ⁠) threshold of zero frequency (i.e. P_i = 0).

• 

• 

• 

• t = the random variable under consideration.

The study area is the City of Wattrelos, France, covering 1,362 hectares with a population of approximately 43,000 inhabitants. The WDS is approximately 162 km in length with the initial layout in 1891. The data used in this research is a 74-year historical dataset.

The pipe network database, including (i) water network characteristics and operational parameters (e.g. variance of pressure) and (ii) failure information with about 424 observations for the period 1991–2004, was compiled by Jafar (2006) and Jafar et al. (2007, 2010) using the GIS.

The pilot WDS consists of 200 pipes with a total length of 17.18 km. The oldest pipe was installed in 1927 while the youngest one was installed in 2002. The first recorded breakage dates to 1937 and the last one to 2005. The dataset selected for the pilot study included 51 cast iron pipes, total length of 4 km, installation year – 1927–1936 (average group installation year – 1931) and diameter (40 mm < D < 100 mm). To analyze the influence of the age (T) on the Failure Rate (F_R), the breakage-recorded data, from 1937 to 2004, were set into nine age-groups of 20-year time-period.

Figure 1(a) illustrates the Probability Distribution (P_i) of the F_Ri values and Figure 1(b) the cumulative probability function for the selected cluster of cast iron pipes and a 20-year group age (1937 to 1956, average group age 15 years). Figure 1(c) shows the reliability function for this group age with increasing F_R values. Exponential regression is used to establish the Weibull shape factor β for the statistical data analysis, yielding for β= 2 the best-fit curve. Figure 1(d) shows that the Maximum Probability Density (P_dmax) remains practically constant with the group age and its corresponding Maximum Probability (P_max) value is quite consistent with the value calculated from Equation (8) for β= 2. Figure 1(a) shows that the Weibull function with β= 2 yields F_Rmax (Equation (7)) and P_max (Equation (8)) values which correspond fairly well to the F_R probability distribution characteristics values.

Figure 2 presents the cumulative probability functions for the F_Ri values for the selected cluster of pipes and the available group ages. It illustrates the relationships among three parameters, including F_Ri, Age (T) and Cumulative Probability (P_Ci). For a constant F_Ri value (e.g. F_Ri = 1) the Cumulative Probability (P_Ci) as well as the Probability (or Risk) of exceeding the selected F_Ri value (i.e. P_Ri = 1 − P_Ci) are therefore a function of the Group Age (T).

For example, the data analysis shows that for a selected value of F_Ri = 1, a 10-year delay in the network rehabilitation from an average group age of 55 years to 64 years will result in a significant risk increase of the probability of exceeding the selected value of F_Ri = 1 from P_Ri = 25% to 60%.

Similarly, for a constant Cumulative Probability (P_Ci) value the F_Ri value is a function of the average group age (T) as illustrated in Figure 2 for P_Ci = 0.6. The relationships between these three fundamental aging parameters could be efficiently used for risk assessment to enable the operator optimizing the WDS asset management.

The ‘Casses’ software, developed by CEMAGREF (Casses Software; Le Gat & Eisenbeis 2000) for analyzing failure data and forecasting breakage risks in water distribution pipelines was used for the data analysis following its three steps of calibration, validation and forecasting. The ‘Casses’ algorithm uses the Poisson model for stochastic data analysis. The model calibration used record data up to 2004, including the validation period of 2000 to 2004, for forecasting the behavior trend over a period extending up to 2055.

Figure 3(a) and 3(b) show respectively the probability distribution of the F_R values and the reliability function forecast for the 20-year time-period group age of 2035 to 2055 (average group age of T = 114 years) for the cast iron pipes.

Figure 3(b) illustrates that the reliability function for this group age corresponds fairly well to the Weibull reliability function with β= 2. Figure 3(a) shows that the Weibull function with β= 2 and = 2.8 yields consistent F_Rmax (Equation (7)) and P_max (Equation (8)) values of the F_R probability distribution.

Figure 3(c) shows the forecast cumulative probability functions obtained for all the average group ages analyzed, indicating that for average group ages of 73 years and 113 years the probability of exceeding a selected F_Ri value of 3 increases, respectively, from P_Ri = 0% to 90%.

The integration of the statistical and stochastic data analyses of the recorded and forecast breakage rates enables the operator to establish a Risk Assessment Methodology (RAM) for optimizing WDS asset management. Figure 4(a) illustrates for constant Cumulative Probability (P_Ci) levels of 20%, 40%, 60% and 80%, the variation of the F_Ri value with the Average Group Age (T) over a time period of 123 years. It shows that for the data of the cast iron pipes, the aging effect starts to significantly increase after 55 years.

Figure 4(b) illustrates for selected F_Ri values of 0, 1, 2, 3, and 4, the risk increase with the network aging through variation of the Probability (P_Ri) of exceeding the selected F_Ri value vs the Average Group Age (T). For example, for a selected value of F_Ri = 1 a delayed rehabilitation of 9 years (from 55 to 64 years) will increase the risk of exceeding the selected value of F_Ri = 1 from 25% to 60%.

The purpose of the proposed Decision Support System (RAM-DSS) is to enable the operator to assess the delayed rehabilitation investment impacts on the risk of exceeding a selected F_Ri value and its cost consequences. For this purpose a risk matrix is defined as the product of the likelihood of exceeding the selected F_R value and the consequences of its occurrence.

For optimizing asset management the consequences could be defined by the selected F_R values for different severity levels of Insignificant, Minor, Moderate, Major, etc. For this pilot study, as illustrated in Table 1, considering a WDS, 4 km long, five severity levels of consequences were identified considering F_R ranges and the related average number of breakages per month. The event likelihood of exceeding a selected F_R value is identified by its frequency of occurrence over the selected time period (or its return period) (Table 2).

Figure 5(a) presents the color-coded risk matrix for the operator's experience-based DSS used for the demo-illustration in this pilot study. As illustrated in Figure 5(b), its deployment can be used for graphic color-coded risk visualization of the Probability (P_Ri) of exceeding a selected F_Ri value. The color-coded risk visualization can be efficiently integrated with multilayer input data on a GIS platform (Jafar 2006; Jafar et al. 2007, 2010) to support risk-based optimization and prioritization of investments in infrastructure repair and rehabilitation for pre-emptive asset management.

The analysis of the relationships between the Failure Rate (F_R) of a water distribution network (or sub-network), the Age (T) of its classified pipes and the Risk (or probability – P_R) of exceeding the selected F_R value have been used in this study to develop and demo-illustrate a Risk Assessment Method Decision Support System (RAM-DSS) for optimizing asset management, forecasting the consequences of delayed rehabilitation and prioritizing the required investments.

The Weibull distribution function, often used for relatively small samples, is used for the statistical data analysis to model the network life-cycle and the risk of exceeding a selected Failure Rate (F_R) as a function of the Age (T). For this case study, the shape factor, representing the degradation rate, remains practically constant with the Group Age (T) and consistently yields the F_Rmax and P_max values of the Probability Density function of the F_R values.

An operator's experience-based risk management matrix is proposed for optimizing WDS asset management. The research demo-illustrates the value of integrating statistical and stochastic data analyses in modeling the vulnerability of the system at a certain age of its life-cycle and forecasting its degradation for preemptive asset management and rehabilitation investment prioritization.

The authors thank Eric Macfarlane, Deputy Commissioner of NYC-DDC, for the fruitful discussions and expert advice during this study as well as Prof. Isam Shahrour for sharing data and our graduate students who contributed to this research.