*Applications of Hierarchical Bayesian Methods to Answer Multilayer Questions with Limited… DOI: http://dx.doi.org/10.5772/intechopen.104784*

means to acquire data on the assets for a condition assessment (buried pipe is not visible and cannot really be assessed). What was found was that for buried infrastructure, much more information was known than anticipated. For one thing, most utilities have a pretty good idea about the pipe materials. Employee memory can be very useful, even if not completely accurate. In most cases, the depth of pipe is fairly similar—the deviations may be known. Soil conditions may be useful—there is an indication that aggressive soil causes more corrosion in ductile iron pipe, and most soil information is readily available. Groundwater is usually known, and if a saltwater interface of a pollution plume exists, it can be mapped and evaluated for impact on pipe. Tree roots will wrap around water and sewer pipes, so their presence is detrimental. Trees are easily noted from aerial photographs. Roads with heavy truck traffic create more vibrations in the soil, causing rocks to move toward the pipe and joints to flex. So, with a little research, there are at least six variables known.

All variable information can be compiled into tables. There is also a need to track events or consequences—breaks, flooding etc.—that would indicate a failure, which is required for predicting future maintenance needs and the most at-risk assets. Finally, the data along with the consequence can be used to predict where the breaks might occur in the future based on past experience. If the break history for a water system, flood records for a stormwater system, or sewer pipe condition from televising is known, the impact of these factors can be developed via a linear regression algorithm. For logistic of linear regression, XLStat® can be used for the statistical analysis. The linear regression algorithm can then be used as a predictive tool to help identify assets that are mostly likely to become a problem.

Data need to be kept up as things change, but exact data are not needed. An example of this type of effort is shown for a medium-sized city in Florida in **Figures 5**–**7**. The City's GIS system was mined for the purposes of this project. Data were retrieved and reviewed to address missing data and clear errors. Nearly 10,000 pipe segments remained. Categorical information on trees, vibrations, soil type, and pipe type is added. Noncategorical data for pipe size, length, and age were also entered. Note that with 10,000 pipe sections and less than 600 breaks, many

**Figure 5.** *Impact of factors on leaks.*

**Figure 6.** *Comparison of predictive and actual breaks over 10 years (correlation desirable).*

pipes have no breaks in their history. The linear regression function for XLStat® was used to create equation to identify the factors associated with each variable and the amount of influence that each exerts (see **Figure 5**). In this case, the equation was:

$$\text{Breaks} = -3.54427 \text{E} - 0\text{\textdegree } -6.5187 \text{E} - 0\text{\textdegree } \* \text{DIA} + 2.607 \text{E} - 0\text{\textdegree } \* \text{Age} \tag{2}$$

It should be noted that this utility has three main types of pipe, installed at three completely different eras. Because the correlation between pipe type and age was high, and likewise pipe type and diameters, other factors that might impact leaks in other communities were not obvious, so other communities would need to recreate this analysis for their situation.

**Figure 6** outlines how the predictive equation correlated for the City's potable water distribution system (well within one standard deviation). **Figure 7** is a GIS map of pipe vulnerability based on the data. Red pipe is the highest priority to schedule for replacement.

The concept should apply to any utility, although the results and factors of concern will be slightly different for each utility. Also, in smaller communities, many variables (ductile iron pipe, PVC pipe, soil condition … ) may be so similar that attempts to differentiate factors may be unproductive.

The analysis indicated two things—that age and AC pipe were correlated.

But what if none of this information is fully known? Many of the indicators of failure can be tracked through the information that is required to be included in the as-built drawings, but what if they are not available? Loss on institutional knowledge through retirements can cost the utility much information on actual pipe diameter, pipe depth, age, and breaks given many utilities do not have extensive work order systems. Other information that might be useful is condition that maintenance crews may have knowledge of. A hierarchical Bayesian model could be developed to address these concerns. Where the pipe is actually known, the categorical variable would be

*Applications of Hierarchical Bayesian Methods to Answer Multilayer Questions with Limited… DOI: http://dx.doi.org/10.5772/intechopen.104784*

**Figure 7.** *Pipe risk—Red pipe is the highest risk for this community, while blue pipes are the lowest risk.*

set to 1. Otherwise, a beta distribution could be developed with a "confidence mean"—we think it is ductile iron, but it might be PVC or cast iron. The same with pipe diameters, etc. As new variables are developed, confidence could be added and priors adjusted. Criticality could be a distribution as well. **Figure 8** shows what an infrastructure assessment Hierarchical Predictive Bayesian model might look like (realizing it might extend far more widely). Currently, research is underway to develop such models, but the data required to create and utilize the models are often lacking even in the most sophisticated organizations.
