A pipe condition assessment model is required to implement effective and economical planned maintenance of the water distribution system. The application of such a model requires sufficient accuracy, which, however, is limited by the complexity of the pipe deterioration process and data storage capacity of the water utility. The majority of previous studies have focused on the improvement of assessment algorithms for data mining. In this study, a mechanistic deterioration point assignment (MDPA) model is developed to make advancements in the modes of data input and result output to enhance the model's accuracy and application scope for cast iron and steel pipes. In this MDPA model, (1) indicators/sub-indicators on external corrosion, external load, internal corrosion, and internal load are constructed and can be obtained by data estimation or techniques and (2) assessment results include both pipe overall condition and detailed conditions on corrosion and load, offering evidence for primary maintenance measures. The weights of the indicators/sub-indicators are estimated using the Bayesian statistics theory. The modelling results of pipe samples demonstrate that this MDPA model is an effective tool for pipe condition assessment.

  • The condition of indicators/sub-indicators of this MDPA model for pipe condition assessment can be obtained either by data estimation or techniques.

  • The MDPA model is capable of exporting pipe detailed conditions for suggesting primary maintenance measures.

  • The MDPA model can be tested or verified by advanced techniques to guarantee model accuracy.

The water distribution system (WDS) typically accounts for 50–80% of the whole construction investment and operating cost of water supply; therefore, it is the most crucial and valuable part. Varied environmental and operational factors deteriorate water pipes, which lead to pipe failures that cause huge water losses, operating cost rises, risks of water quality contamination, and even ground collapses (Wang et al. 2022; Sakai 2024). The American Society of Civil Engineers (2021) report card showed that there was a water main break every 2 min, and 6 billion gallons of treated water were lost every day in the USA. The water loss from the distribution system was about 68.70 billion cubic meters in 2022 in China (Ministry of Housing and Urban-Rural Development 2022). The energy used for water pumping is wasted in translating water to soils or through severely corroded pipes with narrow effective diameters. Water quality contamination risks arise due to the severe corrosion of pipe inner walls or the low pressure owing to negative transients caused by breaks (Qi et al. 2018). Ground collapses may happen due to soil fluidization between high-pressure water and surrounding soils (Latifi et al. 2022a, 2022b). To prevent the above side-effects, it is necessary and economical to identify pipes that mostly need maintenance or replacement before the failure of those pipes (Forero-Ortiz et al. 2023). Therefore, pipe condition is required to help make water asset management decisions and improve the performance of WDSs under limited funding (Forero-Ortiz et al. 2023; Le Gat et al. 2023).

Pipe condition includes structural integrity and its ability to meet service requirements (Opila & Attoh-Okine 2011). Models play a significant role in the research of water pipe condition assessment due to their ability to comprehend the intricate interplay among water, the environment, and pipes (Kleiner & Rajani 2002; Clair & Sinha 2012; Fitchett et al. 2020; Forero-Ortiz et al. 2023). One typical type is the deterioration point assignment (DPA) model, which defines a series of related factors contributing to pipe failure and calculates the relative weight of each factor to obtain a total score to determine pipe condition (Grigg 2006). The DPA models directly establish numerical relationships between pipe condition and relative factors due to management interests, which do not represent the processes of pipe deterioration mechanisms. Different DPA models consist of different combinations of factors (Table 1). Those factors are independent of each other and show certain characteristics of pipes (e.g., age and material) but cannot indicate pipe detailed condition (e.g., corrosion and load). Factors are divided into three categories: physical, environmental, and operational. This classification illustrates the basic logical structure of factors qualitatively and produces no effect on assessment results quantitatively. Several statistical and machine learning algorithms have been adopted in previous literature for weight calibration (Table 1).

Table 1

References on pipe condition assessment using DPA models

FactorsWeight calibration methods and their advantagesReference
AG, CF, DA, DI, GW, LK, MT, OP, PR, ST, TD The analytic hierarchy process provides logical decisions based on analytical methodology and eliminates the chances of challenge. Al-Barqawi & Zayed (2006)  
AG, BD, DI, ER, IP, IQ, MT, OP, ST, PR, TD Artificial neural network is an efficient and cost-saving methodology. Geem et al. (2007)  
AG, BR, CR, DA, DI, GW, LK, MT, IP/OP, PR, WQ, SA, ST, TD The hierarchical fuzzy expert system deals with imprecision and qualitative aspects that are associated with pipe condition. Fares & Zayed (2010)  
AG, BD, DI, ER, IP, IQ, MT, OP, PR, ST, TD Bayesian statistic theory fuses previous studies to obtain a more reliable assessment result. Wang et al. (2010)  
AG, BR, CF, DI, GW, IQ, MT, TD, ST, WQ The Fuzzy analytic network process and Monte Carlo simulation address the interdependency and accumulated uncertainty among factors for accurate and realistic results. El-Abbasy et al. (2019)  
AG, BD, DI, LE, MT, WT Machine learning algorithms are more accurate among known neuro-fuzzy-based methodologies. Elshaboury & Marzouk (2022)  
AG, DI, BR, MP, MT, PR, TJ, WT Monte Carlo simulation delivers advanced optimization and accurate estimation. Dawood et al. (2022)  
FactorsWeight calibration methods and their advantagesReference
AG, CF, DA, DI, GW, LK, MT, OP, PR, ST, TD The analytic hierarchy process provides logical decisions based on analytical methodology and eliminates the chances of challenge. Al-Barqawi & Zayed (2006)  
AG, BD, DI, ER, IP, IQ, MT, OP, ST, PR, TD Artificial neural network is an efficient and cost-saving methodology. Geem et al. (2007)  
AG, BR, CR, DA, DI, GW, LK, MT, IP/OP, PR, WQ, SA, ST, TD The hierarchical fuzzy expert system deals with imprecision and qualitative aspects that are associated with pipe condition. Fares & Zayed (2010)  
AG, BD, DI, ER, IP, IQ, MT, OP, PR, ST, TD Bayesian statistic theory fuses previous studies to obtain a more reliable assessment result. Wang et al. (2010)  
AG, BR, CF, DI, GW, IQ, MT, TD, ST, WQ The Fuzzy analytic network process and Monte Carlo simulation address the interdependency and accumulated uncertainty among factors for accurate and realistic results. El-Abbasy et al. (2019)  
AG, BD, DI, LE, MT, WT Machine learning algorithms are more accurate among known neuro-fuzzy-based methodologies. Elshaboury & Marzouk (2022)  
AG, DI, BR, MP, MT, PR, TJ, WT Monte Carlo simulation delivers advanced optimization and accurate estimation. Dawood et al. (2022)  

Physical factors: AG, age; CF, C factor/Hazen–Williams coefficient; DI, diameter; IP, inner protection; LE, length; MT, material; OP, outer protection; TJ, type of joints; WT, wall thickness.

Environmental factors: BD, buried depth; DA, damage to surroundings/serviced area; ER, electric recharge; GW, groundwater depth; IQ, installation quality; LD, load; ST, soil type.

Operational factors: BR, breakage rate/leakage; CR, cost of repair; MP, maintenance practice; PR, pressure/hydraulic factor; TD, traffic disruption/surface type; WQ, water quality.

The DPA models make good use of various statistical and machine learning algorithms to deal with the complexity and uncertainty of WDSs. While previous studies have been conducted to improve model accuracy by employing novel assessment algorithms to capture the relationship between pipe condition and factors (Al-Barqawi & Zayed 2006; Geem et al. 2007; Fares & Zayed 2010; Wang et al. 2010; El-Abbasy et al. 2019; Dawood et al. 2022; Elshaboury & Marzouk 2022), there are still limitations or challenges in implementing the DPA model in practice as follows: (1) Models demand factor data with reliability and comprehensiveness to ensure the outputs adequately represent pipe condition (Gómez-Martínez et al. 2017; Dawood et al. 2022; Elshaboury & Marzouk 2022). It is hard for some water companies to record whole life cycle data for all the pipes, considering that some factors may vary irregularly for intangible reasons or even difficult to monitor (e.g., traffic load). (2) There exists unnegligible assessment uncertainty due to the complexity and randomness of the pipe deterioration process (Barton et al. 2021; Forero-Ortiz et al. 2023). It is difficult to accurately predict pipe condition, depending on the deterioration patterns of other pipes. Overfitting may happen when the model appears to fit well with the current data but fails to validate with future datasets. (3) Models output total scores for individual pipes while generally ignoring detailed pipe condition (Al-Barqawi & Zayed 2006; Geem et al. 2007; Fares & Zayed 2010; Wang et al. 2010; El-Abbasy et al. 2019; Dawood et al. 2022; Elshaboury & Marzouk 2022), which is important to suggest primary and targeted maintenance measures. The above limitations or challenges restrict the application effect of the DPA models.

Another type of pipe condition assessment method besides models is the techniques that are widely available and commonly used in practice. Acoustic, visual, electromagnetic, ultrasonic, radiographic, and thermographic techniques provide direct insights into pipe condition on integrity, corrosion, load, and indirect elements (e.g. soil condition) (Li et al. 2015; Gnatowski et al. 2021; Latif et al. 2022). Recently, techniques have been combined with intelligent approaches to obtain pipe condition for better accuracy and precision. Wu et al. (2024) used convolutional neural networks to detect and locate pipe leakage based on measured vibrations from a fibre-optic cable. The convolutional neural networks are utilized to handle information obtained by acoustic emission for leak detection and size identification (Ahmad et al. 2023; Siddique et al. 2023). Those studies open new avenues for innovation in condition assessment, demonstrate the application potential of combining techniques and data processing methodologies, and increase the possibility of practical applications for large-scale and complex WDSs.

In this study, a mechanistic DPA (MDPA) model is developed for pipe condition assessment with a similar basic structure to the DPA models. Factors from Table 1 are combined based on the pipe deterioration mechanism to construct indicators/sub-indicators on external corrosion, external load, internal corrosion, and internal load in the MDPA model. Weights of the indicators/sub-indicators are estimated using the Bayesian statistics theory, and then total scores for pipe condition can be obtained. The MDPA model can achieve satisfactory accuracy through (1) an appropriate combination of factors in mechanism constraint due to an in-depth understanding of the relationships between pipe factors and their effects on pipe condition and (2) thoroughfares to techniques to test or verify the precision of assessment results obtained by data estimation. The application scope is enhanced by (1) inputting indicator/sub-indicator conditions through either data estimation or techniques to rid of the requirement of a sizeable high-quality dataset and (2) outputting detailed pipe condition on corrosion and load for targeted maintenance measures. Therefore, the MDPA model can be an effective and convenient tool for implementing pipe management in practice.

Model structure

The structure of the MDPA model used to calculate the pipe condition rate is shown in Equation (1), which is the typical structure of the DPA model.
formula
(1)
where G is the pipe condition rate; i is the serial number of pipe indicator or sub-indicator; I is the total number of indicators/sub-indicator; λ is the weight of the indicator/sub-indicator; Ind is the pipe indicator/sub-indicator.

The assessment objects of this MDPA model are cast iron and steel pipes, which currently occupy 49.9% of the buried pipes in China (China Urban Water Association 2019). The main causes of cast iron and steel pipe deterioration are widely acknowledged to be corrosion and load although entirely explicit mechanisms are still not completely clear because WDSs are buried underground, making it difficult to observe pipe deterioration behaviour (Rajani & Kleiner 2001; Seica & Pacher 2006; Wang et al. 2022). External corrosion includes galvanic, electrolytic, and microbiological corrosion, which reduces pipe residual stress. Internal corrosion leads to hydraulic deterioration including the increase in surface roughness and the reduction in the cross-sectional area, which decreases the sufficient ability of WDSs for adequate pressure, and water quality is also polluted by the galvanic and bacterial action from internal corrosion products (Yamini & Lence 2010). The buried pipe resists load mainly from the external environment of soil and traffic and internal operation pressure.

We construct indicators and sub-indicators by combining factors based on the pipe deterioration mechanism to demonstrate pipe detailed condition. Model input data can be four indicators of external corrosion, external load, internal corrosion, and internal load, or seven sub-indicators of soil effect, pipe external property, soil load, traffic load, pH effect, pipe internal property, and pressure (Figure 1). The factors within the same box construct the same indicators, as indicated by the arrows. Indicators can be split into sub-indicators, and the structures of indicators and sub-indicators are described in Section 2.2.
Figure 1

The indicators (within yellow boxes) and sub-indicators (within blue boxes) constructed by combining factors (within orange boxes).

Figure 1

The indicators (within yellow boxes) and sub-indicators (within blue boxes) constructed by combining factors (within orange boxes).

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Indicators/sub-indicators

External corrosion

Rossum (1969) developed a model to calculate the pit depth of the external wall, which considered soil and pipe properties as influential parameters. It was coincident with the survey that 67% of the respondents pointed out corrosive soils as the primary cause of external corrosion in their systems, 12% believed it was the direct connection of dissimilar metals, and 10% presented coating damage or degradation as the main reason conducted in the USA and Canada (Romer & Bell 2001).

We use Equation (2), disassembled from the model by Rossum (1969), to construct the indicator of external corrosion, which can be split into two sub-indicators such as soil effect (Equation (3)) and pipe external property (Equation (4)).
formula
(2)
where Kn and n are coefficients depending on the soil condition, Kn equals 170, 222, and 355; n equals 1/6, 1/3, and 1/2 when the soil condition is good, fair, and poor, respectively; T is pipe age, year; Kae is a coefficient that depends on pipe material and equals 0.4, 0.9, and 0.6 when pipe material is ductile cast iron, grey cast iron, and steel, respectively; Kpe is a coefficient depending on protection measure and equals 0.5 and 0.9 with and without coating.
formula
(3)
formula
(4)

External load

According to the book on buried pipe design (Moser 2001), the indicator of external load (Equation (5)) on pipes is the sub-indicator of soil (Equation (6)) and traffic load (Equation (7)).
formula
(5)
where Cd is the load coefficient; ρ is the soil density, lb/ft3; Bd is the trench width, ft; t is the pipe wall thickness, ft; K is the surface load coefficient of rigid pavement; D is the pipe external diameter, ft; P is the wheel load, 9,000 lb; F is the impact factor, 1.5.
formula
(6)
formula
(7)

Internal corrosion

The main elements that influence pipe internal corrosion (Equation (8)) are the pH effect (Equation (9)) and the pipe internal property (Equation (10)). Equation (8) is a section of a model to calculate the Hazen–Williams roughness coefficient for cast iron pipes (Sharp & Walski 1988).
formula
(8)
where ap is the roughness growth rate, calculated with the expression of 0.0833 exp (1.9–0.5 pH), ft per year; d is the pipe internal diameter.
Kai is a coefficient that depends on pipe material and equals 0.3, 0.9, and 0.6 when pipe material is ductile cast iron, grey cast iron, and steel, respectively; Kpi is a coefficient depending on the protection measure and equals 0.5 and 0.9 with and without coating.
formula
(9)
formula
(10)

Internal load

Internal load coming from water flow is expressed as Equation (11).
formula
(11)
where p is the water pressure, kg/cm2.
Figure 2 displays some typical techniques that have been used in practice to obtain the detailed information of pipe's external corrosion, soil effect, pipe external properties (Cobb et al. 2012; Wright et al. 2019; Latif et al. 2022), external load, soil load, traffic load (Gnatowski et al. 2021), internal corrosion, pipe internal property (Tohmyoh & Suzuki 2009; Rayhana et al. 2020), pH and internal load (Qi et al. 2018), and techniques that demonstrate pipe condition as leakage or burst (Li et al. 2015; Latif et al. 2022). The condition obtained by detection techniques is available for testing or validating assessment results reached by data analysis of the MDPA model or fed into the MDPA model directly as input data for the indicators/sub-indicators. This helps to conquer the limitations of data requirements in the application of pipe condition assessment models.
Figure 2

Techniques to obtain pipe condition.

Figure 2

Techniques to obtain pipe condition.

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Weight estimation method

The Bayesian statistics theory can be reliably applied with limited data and is capable of providing conceptually sound procedures under uncertainties (Ellison 2004). The parameters are treated as random variables and can be estimated by input observation data and prior knowledge, as shown in Equation (12).
formula
(12)
where θ is the estimation parameter; p(θ) is the prior probability of θ; p(θ|y) is the posterior probability of parameter θ, which is the parameter conditional distribution after data estimation; p(y|θ) is the likelihood function, which represents the occurrence probability of the condition y under different realizations.
The whole operating process of WDS is subject to uncertainty since the process-related factors varied day-to-day, including corrosion rate, load, and velocity (Wang et al. 2010). We use to express the uncertainty of model simulation error of the MDPA model by the Bayesian statistics theory, as shown in Equation (13):
formula
(13)
where ε is the model simulation error, which is assumed to be independent and normally distributed with a mean of zero and variance σ2, εN (0, σ2).
The likelihood function of Equation (13) using the Bayesian statistic theory can be written as Equation (14):
formula
(14)

In this study, the Markov Chain Monte Carlo (MCMC) method is used to generate model posterior distribution. The stationary distribution of the Markov process is the model posterior distribution in Bayesian inference and then the simulation process is run long enough to generate an approximation of the distribution.

Three measures of fit are employed to test the simulation result of the MDPA model.

  • (1) The deviance information criterion (DIC), a larger DIC value reveals a poorer fit between the observations and simulations. The DIC has been used in a variety of literature for models comparing and discussed for improvement (Spiegelhalter et al. 2014). With unknown parameters θ, data y, and the likelihood function P(y|θ), the deviance of a Bayesian model can be shown as follows:
    formula
    (15)

The free number of parameters is defined as follows:
formula
(16)
where is the expectation of θ. is the expectation of D(θ):
formula
(17)
Then DIC is defined with the deviance statistic and the number of free parameters to indicate model fit and complexity.
formula
(18)
  • (2) The coefficient of determination R2 provides a measure of how well the model predicts and is calculated as follows:
    formula
    (19)
    where SSE is the sum of squared errors; SST is the total sum of squares; yi is the observation data; is the mean value of model simulation; is the mean of the observations yi; m is the number of observations.
  • (3) Model error

The data inputted to the MDPA model to generate indicators/sub-indicators weights and perform some statistical analysis used in sections 4.1–4.3 is the same data that was used in Geem et al. (2007) and Wang et al. (2010), which include factor data to construct indicators/sub-indicators and pipe condition rates. Factors include pipe age, diameter, trench depth, inner coating, outer coating, soil density, bedding, number of roads, soil type, pipe material, pH and pressure (Figure 1). Pipe condition rates, ranging from zero to one, are calculated using pipe data on outer corrosion, cracks, pinholes, inner corrosion, and the H–W coefficient, with their weights equalling 0.2. A value of zero means that a pipe is in excellent condition and no maintenance action is needed, while a value of one indicates that a pipe is in critical condition and immediate repair or replacement is required.

The data to make real-world validation is from distribution mains that were buried in communities in a city in northern China and under critical conditions. Detailed information on the data used in this study is provided in Supplementary Materials.

We started with values recommended by previous literature and generated the best values of the indicator/sub-indicator weights using the Bayesian statistic theory. In our study, the indicator/sub-indicator weights are supposed to be normal distributions. Since there were no similar indicators/sub-indicators constructed in previous literature, we added the factor weights relating to the indicators/sub-indicators of the MDPA model together to guide the prior distributions of the weights. The weights of indicator of external corrosion, external load, internal corrosion, and internal load were 0.36, 0.14, 0.24, and 0.06 obtained by Al-Barqawi & Zayed (2006), and 0.4, 0.2, 0.34, and 0.08 obtained by El-Abbasy et al. (2019). Then the prior normal distributions of these four indicators are (0.24, 0.02), (0.1, 0.02), (0.4, 0.02), and (0.15, 0.02) to the MDPA model. The weights of sub-indicators of soil effect, pipe external property, soil load, traffic load, pH effect, pipe internal property, and internal load were 0.13, 0.24, 0.09, 0.05, 0.10, 0.24, and 0.08 obtained by Al-Barqawi & Zayed (2006) and El-Abbasy et al. (2019). Then the prior normal distributions of these seven sub-indicators are (0.2, 0.02), (0.18, 0.02), (0.2, 0.02), (0.2, 0.02), (0.2, 0.02), (0.2, 0.01), and (0.2, 0.01) to the MDPA model. We use the software of WinBUGS (version 1.4.3) to fit data for complex statistic calculation using the Bayesian theory, the calculation process of which is similar to that in the article of Wang et al. (2010).

Fitting of the MDPA model

We use both four indicators and seven sub-indicators to fit condition rates G separately, as described in Equation (1). Most of the pipe condition rates calculated are contained within the 2.5 and 97.5% credible intervals (Crls) as shown in Figure 3. The posterior estimates for the normal distributions of indicator/sub-indicator weight are shown in Table 2, which are comparable to the weights obtained in the articles of Al-Barqawi & Zayed (2006) and El-Abbasy et al. (2019) shown in the previous paragraph. The detailed condition of corrosion and load is demonstrated by condition rates of indicators and sub-indicators, and water utilities can take targeted measures. More attention should be paid to external corrosion monitoring of pipe 5 since external corrosion condition is worse than external load, internal corrosion, and internal load condition (Figure 4(a)). This situation is nearly equally due to soil effect and pipe external property since those two sub-indicators obtain similar condition rates (Figure 4(b)). No maintenance action is required due to its low condition rate, as shown in Figure 3.
Table 2

Indicator/sub-indicator weights of the MDPA model

Indicator/sub-indicatorWeight
R2DIC
Mean2.5%97.5%
External corrosion 0.46 0.29 0.61 0.72 − 18.38 
External load 0.37 0.22 0.51 
Internal corrosion 0.33 0.16 0.33 
Internal load 0.13 0.01 0.35 
Soil effect 0.20 0.03 0.38 0.78 − 22.56 
Pipe external property 0.23 0.06 0.40 
Soil load 0.13 0.01 0.31 
Traffic load 0.12 0.01 0.27 
pH effect 0.19 0.02 0.39 
Pipe internal property 0.12 0.01 0.29 
Internal load 0.23 0.050 0.41 
Indicator/sub-indicatorWeight
R2DIC
Mean2.5%97.5%
External corrosion 0.46 0.29 0.61 0.72 − 18.38 
External load 0.37 0.22 0.51 
Internal corrosion 0.33 0.16 0.33 
Internal load 0.13 0.01 0.35 
Soil effect 0.20 0.03 0.38 0.78 − 22.56 
Pipe external property 0.23 0.06 0.40 
Soil load 0.13 0.01 0.31 
Traffic load 0.12 0.01 0.27 
pH effect 0.19 0.02 0.39 
Pipe internal property 0.12 0.01 0.29 
Internal load 0.23 0.050 0.41 
Figure 3

Results of the MDPA model constructed by four indicators (purple) and seven sub-indicators (green).

Figure 3

Results of the MDPA model constructed by four indicators (purple) and seven sub-indicators (green).

Close modal
Figure 4

Results of the indicators (a)/sub-indicators (b).

Figure 4

Results of the indicators (a)/sub-indicators (b).

Close modal

We examined the prior rationality of the MDPA model by doubling (i.e., cutting the variance) and cutting (i.e., increasing the variance) in half the precision of the input priors. The former examinations lead to a slightly better coefficient of determinations of 0.80 and 0.75 when input data are 7 sub-indicators and 4 indicators, while the latter examinations lead to significant reductions in fitting effect. The above results indicate that the prior probabilities selected by the MDPA model meet the assessment requirements and can ensure simulation accuracy. The ranges of the priors are neither too wide to induce easy formation of multiple optimization values nor too narrow to induce difficulty in computing the optimal solution.

Evaluations of the indicators/sub-indicators

We estimated the weights of pipe indicators/sub-indicators individually to evaluate their statistical impact on model performance through numerical experiments on the MDPA model. For these tests, the weight of one indicator/sub-indicator was estimated and the weights of the remaining four indicators/six sub-indicators were assigned fixed values. As Table 3 shows, there is no significant difference in goodness of fit among all tests with similar model error uncertainties. These findings can be interpreted as evidence that pipe condition rates are equally sensitive to the prior distribution specifications of indicators/sub-indicators, meaning that the range of predicted output is affected nearly equally by the distributions of input indicators/sub-indicators. The reasons for this ‘similar’ predictive model error can be that prior specification change of the indicators/sub-indicators may not lead to an exploration of suboptimal regions of the model posterior, and no relationship between the indicators/sub-indicators and pipe condition rates is particularly steeper or higher order than others.

Table 3

Goodness of fit for numerical experiments of indicators/sub-indicators

Indicator/sub-indicatorModel error
R2
Mean2.5%97.5%
External corrosion 0.14 0.10 0.21 0.70 
External load 0.14 0.11 0.20 0.69 
Internal corrosion 0.14 0.11 0.21 0.71 
Internal load 0.14 0.11 0.21 0.65 
Soil effect 0.14 0.11 0.21 0.72 
Pipe external property 0.14 0.11 0.21 0.72 
Soil load 0.13 0.10 0.19 0.75 
Traffic load 0.13 0.10 0.19 0.70 
pH effect 0.14 0.11 0.20 0.76 
Pipe internal property 0.13 0.10 0.19 0.75 
Internal load 0.14 0.11 0.20 0.72 
Indicator/sub-indicatorModel error
R2
Mean2.5%97.5%
External corrosion 0.14 0.10 0.21 0.70 
External load 0.14 0.11 0.20 0.69 
Internal corrosion 0.14 0.11 0.21 0.71 
Internal load 0.14 0.11 0.21 0.65 
Soil effect 0.14 0.11 0.21 0.72 
Pipe external property 0.14 0.11 0.21 0.72 
Soil load 0.13 0.10 0.19 0.75 
Traffic load 0.13 0.10 0.19 0.70 
pH effect 0.14 0.11 0.20 0.76 
Pipe internal property 0.13 0.10 0.19 0.75 
Internal load 0.14 0.11 0.20 0.72 

Uncertainty reduction from the prior to the posterior distributions of the indicators/sub-indicators can reflect the soundness of their prior characterization. The difference between updating traces can indicate the perception of the estimation of indicators/sub-indicators. It can determine which indicators/sub-indicators can be reasonably delineated through an inverse solution exercise or which one warrants direct estimation (Arhonditsis et al. 2007). From estimation results, the variation coefficients (standard deviation⁄ mean value) of external corrosion, external load, internal corrosion, and internal load are reduced from 0.30, 0.37, 0.47, and 0.79 to 0.18, 0.20, 0.27, and 0.69, respectively; the variation coefficients of soil effect, external pipe property, soil load, traffic load, pH effect, internal pipe property, and internal load are reduced from 0.70, 0.78, 0.70, 0.70, 0.70, 0.70, and 0.59 to 0.45, 0.38, 0.64, 0.52, 0.58, 0.60, and 0.41, respectively. The prior and posterior distributions of the indicators/sub-indicators are shown in Figure 5. All the variation coefficients are reduced from the prior distributions to the posterior distributions, and there is no substantial difference among the variation coefficients. Thus, the weight estimation of all the indicators/sub-indicators of the MDPA model needs statistical calculation besides expert experience.
Figure 5

Prior (orange) and posterior (blue) distributions of the indicator/sub-indicator weights of the MDPA model.

Figure 5

Prior (orange) and posterior (blue) distributions of the indicator/sub-indicator weights of the MDPA model.

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Comparison between the MDPA and DPA models

We compare the MDPA model to a DPA model in terms of fitting effects, construction characteristics, and application conditions. The structure, simulating steps, and input data of factor (Table 1), and condition rates of the DPA model are the same as the article published by Wang et al. (2010). It means this DPA model has the same input factor data as the MDPA model. The fitting effects of the MDPA and DPA models are shown in Figure 6. The MDPA model (seven sub-indicators) shows a slightly higher assessing accuracy with a better R2 value of 0.78 than 0.75 of the DPA model. One reason for this result should be the appropriate combination of pipe factors in the MDPA model. Taking the factor of age as an example, the MDPA model constructs a positive exponential relationship between age and pipe external corrosion, which is more conforming to the pipe deterioration process as the bath curve described. In contrast, the relationship between the age and model output using the DPA method is purely a linear function, which is not the actual pipe deterioration pattern. Therefore, the MDPA model achieves better accuracy with fewer model variables since the DPA model has 11 input factors and the MDPA model has 7 input sub-indicators. The detailed condition of pipe corrosion and load is outputted by the MDPA model, as shown in Figure 4(b) in section 4.1, while the DPA model can only output a total score for the whole pipe.
Figure 6

Fitting results of the MDPA model and the DPA model.

Figure 6

Fitting results of the MDPA model and the DPA model.

Close modal

Data requirements are one of the main limitations in the application of pipe condition assessment models. This MDPA model can obtain input data either from pipe factor data or techniques. If critical data of a pipe are missing in the database, e.g. no pipe age data, pipe condition can be obtained in a novel way that the detailed condition of pipe corrosion is detected by techniques and the detailed condition of pipe load is calculated by Equations (6) and (7) to conquer the obstacle of insufficient pipe factor data. Besides serving as a means of obtaining pipe data, techniques can be used to test or verify the accuracy of assessment results and the structure of indicators/sub-indicators.

A case study of the MDPA model

We validate the application effect of the MDPA model using pipe data from buried distribution mains in communities. From the assessment result, pipes 1–5, 7, and 9–13 obtain high condition rates, indicating that those pipes are in critical condition (Figure 7). The condition rates of internal and external corrosion of those pipes are high to show poor condition, and the condition rates of external and internal load are not high and show good condition (Figure 8(a)). The main reasons for poor external corrosion condition include both soil effect and pipe external property, and the main reasons for poor internal corrosion condition are both pH effect and pipe internal property (Figure 8(b)). Considering that those pipes have high total scores and need massive maintenance tasks that both internal and external anti-corrosion measures are required, the best maintenance plan for those pipes would be replaced as soon as possible. Pipes 6, 8, 14, and 15 obtain lower condition rates (Figure 7), then those pipes can continue to be used or be maintained by some anti-corrosion measures to extend their effective service lives (Figure 8(a)).
Figure 7

Results of the MDPA model constructed by four indicators (purple) and seven sub-indicators (green).

Figure 7

Results of the MDPA model constructed by four indicators (purple) and seven sub-indicators (green).

Close modal
Figure 8

Results of the indicators (a)/sub-indicators (b).

Figure 8

Results of the indicators (a)/sub-indicators (b).

Close modal

Seventy-three per cent of pipes obtained assessment rates higher than 0.7 (Figure 7), which aligns with the fact that all the pipes were in critical condition. There are assessment errors for pipes 6, 8, 14, and 15 with the output results of good condition. The detailed condition output from this MDPA model provides a basis for water utilities to decide what measures should be taken to address what problems. The modelling results of those pipe samples suggest that this MDPA model is an effective pipe condition assessment tool.

The structure of the indicators/sub-indicators of the MDPA model in this study is from classic mechanism models, which can be further improved and revised through the advancements in the pipe deterioration process promoted by emerging approaches. Finite element analysis has been utilized to elaborate local flow properties and grab complex interactions among mechanical stress, material properties, and environmental factors. The transient wave behaviours and wall shear stress can be investigated, and stress corrosion cracking can be predicted with better accuracy and efficiency (Zhang et al. 2022; Sarwar et al. 2024).

The selection of techniques depends on pipe material, diameter, pressure, velocity, types of defects, environmental factors, and the size of WDS. To improve the MDPA model, the application conditions of techniques need to be further summarized. How to use techniques to verify assessment results based on data estimation also requires organization. We obtain wrong assessment results for pipe samples in the case in this section, which may be avoided by proper integration with techniques.

More importantly, additional validation analyses on various WDSs should be conducted to accumulate and summarize practical experience. We believe water utilities can apply the MDPA model in a reasonable framework to integrate statistical analysis and techniques, depending on the practical situation of data storage, cost of techniques, and accuracy requirements.

Pipe condition assessments are required for effective and economical planned maintenance to help water utilities rehabilitate hydraulic capacity, reduce operating costs, and guarantee water quality in WDSs. For the better employment of both pipe data and techniques, a MDPA model is developed in our study and provides advantages in two main ways: (1) the accuracy of indicator/sub-indicator inputted in the MDPA model can be tested or verified by advanced geophysical or sensing techniques, which integrates pipe detection techniques to guarantee model accuracy; (2) the indicators/sub-indicators are constructed from factors based on the pipe failure mechanism, while it can prevent illogical errors arising from purely data-driven methodologies and can also demonstrate pipe detailed conditions on corrosion and load to enrich assessment outputs.

The modelling results of pipes samples show that this MDPA model can output accurate pipe overall and detailed condition. The MDPA model can be flexibly and broadly applied by water utilities with the advantages of indicating detailed information on pipe condition, linking detection techniques, and requiring a small amount of input data.

Future research directions to enhance the MDPA model include the improvement of indicator/sub-indicator structures and the application principles of techniques. It is crucial to ensure that the indicators/sub-indicators represent detailed pipe conditions precisely in suitable structures in various network size, burying technologies, and surrounding environment. There is still much work to be done to clarify how techniques can be effectively utilized in the MDPA model for excellent accuracy and economical investment. Additional validations on various WDSs are anticipated to support the aforementioned research work for expanding the application scope of the MDPA model.

This work was supported by the project funded by the National Natural Science Foundation of China (Grant No. 52200116).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Ahmad
Z.
,
Nguyen
T.
&
Kim
J.
2023
Leak detection and size identification in fluid pipelines using a novel vulnerability index and 1-D convolutional neural network
.
Engineering Applications of Computational Fluid Mechanics
17
(
1
),
2165159
.
doi:10.1080/19942060.2023.2165159
.
Al-Barqawi
H.
&
Zayed
T.
2006
Assessment model of water main conditions
. In:
The Pipeline Division Specialty Conference
,
30 July–2 August
,
Chicago, IL, USA
.
doi:10.1061/41138(386)5
.
American Society of Civil Engineers
.
2021
2021 Report Card for America's Infrastructure
.
Available from: https://infrastructurereportcard.org/. (accessed 5 February 2024)
.
Arhonditsis
G. B.
,
Qian
S. S.
,
Stow
C. A.
,
Lamon
C. E.
&
Reckhow
K. H.
2007
Eutrophication risk assessment using Bayesian calibration of process-based models: Application to a mesotrophic lake
.
Ecological Modelling
28
(
2–4
),
215
229
.
doi:10.1016/j.ecolmodel.2007.05.020
.
Barton
N. A.
,
Hallett
S. H.
&
Jude
S. R.
2021
The challenges of predicting pipe failures in clean water networks: A view from current practice
.
Water Supply
22
(
1
),
527
541
.
doi:10.2166/ws.2021.255
.
China urban water association
.
2019
China Urban Water Supply Statistical Yearbook 2019
.
China Urban Water Association
,
Beijing, China
.
Clair
A. S.
&
Sinha
S.
2012
State-of-the-technology review on water pipe condition, deterioration and failure rate prediction models
.
Urban Water Journal
9
(
2
),
85
112
.
doi:10.1080/1573062X.2011.644566
.
Cobb
A. C.
,
Kwun
H.
,
Caseres
L.
&
Janega
G.
2012
Torsional guided wave attenuation in piping from coating, temperature, and large-area corrosion
.
NDT & E International
47
,
163
170
.
doi:10.1016/j.ndteint.2012.01.002
.
Dawood
T.
,
Elwakil
E.
,
Novoa
H. M.
&
Delgado
J. F. G.
2022
Watermain's failure index modeling via Monte Carlo simulation and fuzzy inference system
.
Engineering Failure Analysis
134
,
106100
.
doi:10.1016/j.engfailanal.2022.106100
.
El-Abbasy
M. S.
,
Zayed
T.
,
El-Chanati
H.
,
Mosleh
F.
,
Senouci
A.
&
Al-Derham
H.
2019
Simulation-based deterioration patterns of water pipelines
.
Structure and Infrastructure Engineering
15
(
7
),
965
982
.
doi:10.1080/15732479.2019.1599965
.
Ellison
A. M.
2004
Bayesian inference in ecology
.
Ecology Letters
7
(
6
),
509
520
.
doi:10.1111/j.1461-0248.2004.00603.x
.
Elshaboury
N.
&
Marzouk
M.
2022
Prioritizing water distribution pipelines rehabilitation using machine learning algorithms
.
Soft Computing
26
(
11
),
5179
5193
.
doi:10.1007/s00500-022-06970-8
.
Fares
H.
&
Zayed
T.
2010
Hierarchical fuzzy expert system for risk of failure of water mains
.
Journal of Pipeline Systems Engineering and Practice
1
(
1
),
53
62
.
doi:10.1061/(ASCE)PS.1949-1204.0000037
.
Fitchett
J. C.
,
Karadimitriou
K.
,
West
Z.
&
Hughes
D. M.
2020
Machine learning for pipe condition assessments
.
Journal American Water Works Association
112
(
5
),
50
55
.
doi:10.1002/awwa.1501
.
Forero-Ortiz
E.
,
Martinez-Gomariz
E.
,
Sanchez-Juny
M.
,
Gonzalez
J. C.
,
Cucchietti
F.
,
Viader
F. B.
&
Monton
M. S.
2023
Models and explanatory variables in modelling failure for drinking water pipes to support asset management: A mixed literature review
.
Applied Water Science
13
(
11
),
210
.
doi:10.1007/s13201-023-02013-1
.
Geem
Z. W.
,
Tseng
C.
,
Kim
J.
&
Bae
C.
2007
Trenchless water pipe condition assessment using artificial neural network
. In:
Pipelines 2007: Advances and Experiences with Trenchless Pipeline Projects
,
8–11 July
,
Boston, MA, United States
.
doi:org/10.1061/40934(252)26
.
Gnatowski
A.
,
Kijo-Kleczkowska
A.
,
Chyra
M.
&
Kwiatkowski
D.
2021
Numerical-experimental analysis of polyethylene pipe deformation at different load values
.
Materials
14
(
1
),
160
.
doi:10.3390/ma14010160
.
Gómez-Martínez
P.
,
Cubillo
F.
,
Martín-Carrasco
F.
&
Garrote
L.
2017
Statistical dependence of pipe breaks on explanatory variables
.
Water
9
(
3
),
158
.
doi:10.3390/w9030158
.
Grigg
N. S.
2006
Condition assessment of water distribution pipes
.
Journal of Infrastructure Systems
12
(
3
),
147
153
.
doi:10.1061/(ASCE)1076-0342(2006)12:3(147)
.
Kleiner
Y.
&
Rajani
B.
2002
Forecasting variations and trends in water-main breaks
.
Journal of Infrastructure Systems
8
(
4
),
122
131
.
doi:10.1061/(ASCE)1076-0342(2002)8:4(122)
.
Latif
J.
,
Shakir
M. Z.
,
Edwards
N.
,
Jaszczykowski
M.
,
Ramzan
N.
&
Edwards
V.
2022
Review on condition monitoring techniques for water pipelines
.
Measurement
193
,
110895
.
doi:10.1016/j.measurement.2022.110895
.
Latifi
M.
,
Mohammadbeigi
S.
,
Farahi Moghadam
K.
,
Naeeni
S. T. O.
&
& Kilanehei
F.
2022a
Experimental study of pressure and soil effects on fluidization and mobile bed zones around buried leaking pipes
.
Journal of Pipeline Systems Engineering and Practice
13
(
4
),
04022034
.
doi:10.1061/(ASCE)PS.1949-1204.0000671
.
Latifi
M.
,
Parvaneh
R.
&
Naeeni
S. T.
2022b
Investigating the influence of surrounding soil properties on leakage discharge from cracks in polyethylene pipes
.
Engineering Failure Analysis
141
,
106676
.
doi:10.1016/j.engfailanal.2022.106676
.
Le Gat
Y.
,
Curt
C.
,
Werey
C.
,
Caillaud
K.
,
Rulleau
B.
&
Taillandier
F.
2023
Water infrastructure asset management: State of the art and emerging research themes
.
Structure and Infrastructure Engineering
.
doi:10.1080/15732479.2023.2222030
.
Li
R.
,
Huang
H.
,
Xin
K.
&
Tao
T.
2015
A review of methods for burst/leakage detection and location in water distribution systems
.
Water Science and Technology – Water Supply
15
(
3
),
429
441
.
doi:10.2166/ws.2014.131
.
Ministry of Housing and Urban-Rural Development
2022
China Urban Water Supply Statistical Yearbook 2022
. .
Moser
A. P.
2001
Buried Pipe Design
(2nd edn).
McGraw-Hill, New York
,
USA
.
Opila
M. C.
&
Attoh-Okine
N.
2011
Novel approach in pipe condition scoring
.
Journal of Pipeline Systems Engineering and Practice
2
(
3
),
82
90
.
doi:10.1061/(ASCE)PS.1949-1204.0000081
.
Qi
Z.
,
Zheng
F.
,
Guo
D.
,
Maier
H. R.
,
Zhang
T.
,
Yu
T.
&
Sha
Y.
2018
Better understanding of the capacity of pressure sensor systems to detect pipe burst within water distribution networks
.
Journal of Water Resources Planning and Management
144
(
7
),
04018035
.
doi:10.1061/(ASCE)WR.1943-5452.0000957
.
Rajani
B. B.
&
Kleiner
Y.
2001
Comprehensive review of structural deterioration of water mains: Physically based models
.
Urban Water Journal
3
(
3
),
151
164
.
doi:10.1016/S1462-0758(01)00032-2
.
Rayhana
R.
,
Jiao
Y.
,
Zaji
A.
&
Liu
Z.
2020
Automated vision systems for condition assessment of sewer and water pipelines
.
IEEE Transactions on Automation Science and Engineering
18
(
4
),
1861
1878
.
doi:10.1109/TASE.2020.3022402
.
Romer
A. E.
&
Bell
G.
2001
Causes of external corrosion on buried water mains
. In:
Pipelines 2001: Advances in Pipelines Engineering and Construction
,
San Diego, CA, USA
,
15–18 July
.
Rossum
J. R.
1969
Prediction of pitting rates in ferrous metals from soil parameters
.
Journal American Water Works Association
61
,
305
310
.
doi:10.2307/41266103
.
Sakai
H.
2024
Review of research on performance indicators for water utilities
.
AQUA – Water Infrastructure Ecosystems and Society
73
(
2
),
167
182
.
https://doi.org/10.2166/aqua.2024.224
.
Sarwar
U.
,
Mokhtar
A. A.
,
Muhammad
M.
,
Wassan
R. K.
,
Soomro
A. A.
,
Wassan
M. A.
&
Kaka
S.
2024
Engineering Applications of Computational Fluid Mechanics
18
(
1
),
2302906
.
doi:10.1080/19942060.2024.2302906
.
Seica
A. M.
&
Pacher
A. J.
2006
Simplified numerical method to evaluate the mechanical strength of cast iron water pipes
.
Journal of Infrastructure Systems
12
(
1
),
60
67
.
doi:10.1061/(ASCE)1076-0342(2006)12:1(60)
.
Sharp
W. W.
&
Walski
T. M.
1988
Predicting internal roughness in water mains
.
Journal American Water Works Association
80
(
11
),
34
40
.
doi:10.2307/41292059
.
Siddique
M. F.
,
Ahmad
Z.
&
Kim
J.
2023
Pipeline leak diagnosis based on leak-augmented scalograms and deep learning
.
Engineering Applications of Computational Fluid Mechanics
17
(
1
),
2225577
.
doi:10.1080/19942060.2023.2225577
.
Spiegelhalter
D. J.
,
Best
N. G.
,
Carlin
B. P.
&
Linde
A.
2014
The deviance information criterion: 12 years on
.
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
76
(
3
),
485
493
.
doi:10.1111/rssb.12062
.
Tohmyoh
H.
&
Suzuki
M.
2009
Measurement of the coating thickness on the back side of double-sided coated structures by means of acoustic resonant spectroscopy
.
Surface & Coatings Technology
204
(
4
),
546
550
.
doi:10.1016/j.surfcoat.2009.08.040
.
Wang
C.
,
Niu
Z.
,
Jia
H.
&
Zhang
H.
2010
An assessment model of water pipe condition using Bayesian inference
.
Journal of Zhejiang University – SCIENCE A
11
(
7
),
495
504
.
doi:10.1631/jzus.A0900628
.
Wang
C.
,
Xu
Q.
,
Zhou
Y.
&
Qiang
Z.
2022
Research on pipe burst in water distribution systems: Knowledge structure and emerging trends
.
AQUA – Water Infrastructure Ecosystems and Society
71
(
12
),
1408
1424
.
https://doi.org/10.2166/aqua.2022.150
.
Wright
R. F.
,
Lu
P.
,
Devkota
J.
,
Lu
F.
,
Ziomek-Moroz
M.
&
Ohodnicki
P. R.
2019
Corrosion sensors for structural health monitoring of oil and natural gas infrastructure: A review
.
Sensors
19
(
18
),
3964
.
doi:10.3390/s19183964
.
Wu
H.
,
Duan
H.
,
Lai
W. W. L.
,
Zhu
K.
,
Cheng
X.
,
Yin
H.
,
Zhou
B.
,
Lai
C.
,
Lu
C.
&
Ding
X.
2024
Leveraging optical communication fiber and AI for distributed water pipe leak detection
.
IEEE Communications Magazine
62
(
2
),
126
132
.
doi:10.1109/MCOM.003.2200643
.
Yamini
H.
&
Lence
B. Y.
2010
Probability of failure analysis due to internal corrosion in cast-iron pipes
.
Journal of Infrastructure Systems
16
(
1
),
73
80
.
doi:10.1061/(ASCE)1076-0342(2010)16:1(73)
.
Zhang
Y.
,
Duan
H.
&
Keramat
A.
2022
CFD-aided study on transient wave-blockage interaction in a pressurized fluid pipeline
.
16
(
1
),
1957
1973
.
doi:10.1080/19942060.2022.2126999
.
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