Optimization of long-term renewal investment plan for drinking water conveyance networks using dynamic programming

One critical component of social overhead capital, essential for human survival, is the transmission and conveyance pipes of the drinking water supply systems. These pipes deteriorate over time due to various physical, environmental, and operational factors (Kleiner & Rajani 2002). The deterioration of water pipes undermines the original purpose of delivering safe, high-quality tap water with consistent pressure without insufficient quantity. Furthermore, the deterioration of water pipes can lead to structural problems, resulting in direct and indirect losses and potentially damaging other infrastructure (Abdel-Mottaleb et al. 2019; Assad & Bouferguene 2021). Therefore, ensuring proper installation, conducting regular inspections, and performing repair and maintenance tasks, including cleaning, replacement, or rehabilitation throughout the pipe's lifespan, are crucial to maintaining the performance of buried pipes above the target level. Additionally, water utilities require an investment plan to systematically execute these tasks within limited resources.

Dandy & Engelhardt (2006) proposed a comprehensive approach to developing a water pipe renewal plan, emphasizing three crucial factors: structural safety of the pipes, economic efficiency of renewal, and water quality. Among three factors, water quality mainly relates to replacing small-diameter distribution pipes with extended residence times. Therefore, when replacing large-diameter transmission or conveyance pipes, greater emphasis is placed on the structural safety of the pipes and the economic efficiency of renewal rather than water quality. As the water transmission and conveyance network represent most of the expenses needed to maintain the water supply system, water utility managers facing budget constraints must opt for the most cost-effective investment alternative (Kleiner & Rajani 2022). Nonetheless, in practical scenarios, managers traditionally employ a less efficient approach, wherein they replace pipes that have exceeded a predetermined period of use or replace a set percentage of pipes annually (Fitchett et al. 2020). Traditional methods not only lead to inefficient allocation of limited resources but also pose challenges for ensuring the long-term sustainability of the water supply system (Taiwo et al. 2023).

Regarding predicting the appropriate renewal period for water pipes, methods can generally be categorized into two approaches: physical condition assessment and statistical analysis. The physical approach involves diagnosing the structural characteristics of the pipes, such as corrosion depth and material degradation, to predict lifespan (Kleiner & Rajani 2001). For example, models like the safety factor (SF) concept evaluate structural safety by examining the relationship between residual tensile strength and applied load (Deb et al. 2002). Recent advancements include artificial neural network (ANN) models to predict corrosion depth accurately (Kim et al. 2023). On the other hand, statistical approaches analyze historical damage and leakage data to predict future failure rates. These methods range from early age-based models (Shamir & Howard 1979) to more advanced machine learning techniques, such as random forest and support vector machines (Giraldo-Gonzalez & Rodriguez 2020). Recent studies have further refined these methods by addressing challenges such as imbalanced datasets. For example, Beig Zali et al. (2024) proposed a semi-supervised clustering approach to enhance classification accuracy in pipe failure prediction by leveraging domain knowledge with unsupervised learning, demonstrating superior performance compared with traditional class imbalance techniques. Although machine learning methods have improved predictive accuracy, challenges remain due to real-time condition assessment data limitations and the potential mismatch between model predictions and actual pipe conditions.

Various decision support systems have been developed to address the challenges faced thus far. Most systems utilize methods for predicting an appropriate renewal time, which can be based on factors such as failure rates, service life, or the life cycle cost of the pipe. Loganathan et al. (2002), Shin et al. (2016), and Zhang et al. (2019) recommend replacing the pipe when it reaches a specific time threshold. Other approaches involve prioritizing pipe replacements based on risk assessments, reliability indices, or the condition assessment score of the pipes (Rahman et al. 2014; Haider et al. 2015; De Sousa-Pereira et al. 2020). Alternatively, some systems focus on replacing pipes to meet reliability or key performance indicators (Alegre et al. 2014; Liu et al. 2020).

Unfortunately, because the methods proposed to date approach pipe renewal from an incomplete perspective, the advantages or applicability of a method that simultaneously considers various aspects are unknown. As previous researchers have mentioned, determining the timing of pipe renewal by comprehensively considering various elements ensures the sustainability of water utilities. This study specifically focuses on creating a method that facilitates investment decisions for renewing over 500 mm large-diameter conveyance pipe networks, primarily addressing structural safety and economic efficiency. To this end, this study developed ANN-based models for predicting corrosion depth to estimate the structural safety of pipes and ANN-based models to predict failure rate for assessing the economic efficiency of pipe renewal. Based on the developed two prediction models, a dynamic programming (DP)-based method was designed to optimize the renewal investment of the conveyance pipe network. This method minimizes the life cycle cost of the entire network while working within the financial constraints of the water utility. By applying this developed method to a real-world network, this study demonstrates its practicality in supporting investment decisions related to renewal. This proposed management strategy empowers decision-makers to pinpoint the ideal time for pipe renewal, all while effectively minimizing costs and ensuring the safety of pipes.

This study developed ANN-based corrosion prediction models to acquire a corrosion ratio for calculating the SF. The choice of ANN was driven by its ability to capture complex, non-linear relationships between variables, making it particularly suitable for datasets with intricate patterns. ANN is more adept at learning from multidimensional data where multiple interacting factors influence the outcome. In developing these models, this study utilized pitting corrosion depth data collected from specimens of pipes with a diameter of 500 mm or more from various locations in the Republic of Korea spanning the years 1980 to 2021. During an analysis of collected data, any corrosion depth measurements that registered as 0 mm or exceeded the standard pipe thickness were identified as outliers and subsequently excluded from the sample. Table 1 shows the detailed number of remaining samples after removing outliers.

The output of prediction models was designated to represent corrosion depth, while inputs encompassed pipe-related information, including pipe age, pipe diameter, and factors influencing corrosion depth. Model training and validation datasets were partitioned in an 8:2 ratio, with data from the study area reserved for model testing. To determine hyperparameters of models, this study conducted a grid search, a method that exhaustively explores parameter combinations in a structured manner. Hyperparameters subjected to this search included the number of hidden layers (ranging from 2 to 5), the number of nodes in hidden layers (ranging from 2 to 7), learning rate (10⁻², 10⁻³, 10⁻⁴, and 10⁻⁵), and threshold (10⁻¹, 10⁻², 10⁻³, and 10⁻⁴). The sigmoid function was employed as the activation function. Additionally, this study adopted an early stopping technique to prevent overfitting. This technique halts the training process at a specific point during the epoch repetition. The chosen early stopping criterion was when the validation error trend shifted from decreasing to increasing. After predicting the corrosion depth of a pipe within a specific environment and age using corrosion prediction models, a residual strength was calculated according to Equation (2). The method for calculating the applied stress is detailed in the supplementary material.

Failure rate prediction models, essential for benefit calculation, were also constructed using an ANN, similar to corrosion prediction models addressed earlier. To build these models, failure history data from pipes with a diameter of 500 mm or more from 1980 to 2021 across the Republic of Korea was utilized. Failures caused by external factors were excluded from the failure history data. Table 2 shows the number of samples and collected data for developing failure rate prediction models. Unlike corrosion prediction models, all available failure data without excluding outliers were included. The model's output was designated as a failure rate, while its input consisted of pipe-related data such as age, diameter, and other pertinent factors. The model development approach mirrored that used for corrosion prediction models.

Water pipe failures can be categorized into circular breaks, joint failures, longitudinal failures, and corrosion, with various contributing factors (Barton et al. 2019). Additionally, the size of the failure may vary depending on whether the installation process is appropriate (Grigg 2017), making it reasonable to employ distinct maintenance techniques depending on the failure's magnitude (Taiwo et al. 2023). Nevertheless, realistically predicting the size of failures, such as leaks, bursts, deflections, bends, corrosion pits, and circumferential cracks, is a formidable challenge. Consequently, this study establishes a plan assuming that pipes identified as prone to damage by the failure prediction model will be repaired and used. In contrast, pipes with SF below 1.0 will be replaced.

One rule and one restriction were established for planning. A rule determines which pipes are eligible for renewal and consists of two selection options. The first selection option takes into account the safety of the pipes. Renewal is not considered when the SF at a specific point in time is greater than 3.0. Replacement is an option when the SF ranges from 1.0 to 3.0, and pipes are unquestionably replaced when the SF falls below 1.0. The second selection option pertains to the cost efficiency of renewal. Renewal is not carried out when the BC at a specific point in time is less than 1.0, but it is pursued when the BC exceeds 1.0. Although pipes should be replaced when the SF is less than 1.0, there may be cases where renewal cannot be performed due to a BC less than 1.0. This study prioritizes the SF standard over the BC standard to prevent such problems from occurring.

This study set analysis scenarios to compare the developed method with other methods, as shown in Table 3.

To obtain an optimal renewal plan that fulfills the objective function and constraint conditions, this study develops a coded program using Microsoft Visual C + +. Initially, the program calculates the number of cases meeting the SF requirements for each pipe and the economic evaluation results by aggregating the annual instances. The program then assesses whether the total costs incurred across all pipes satisfy the constraints. Furthermore, it carries over the number of compliant cases for examination to the following year. This iterative process continues until the predetermined endpoint is reached, ultimately yielding the minimum life cycle cost for all pipes as the optimal solution.

This study developed ANN-based corrosion and failure rate prediction models using corrosion and failure-related data and pipe characteristic data collected throughout the Republic of Korea.

As a result of utilizing the average values of factors influencing corrosion to predict corrosion depth, models demonstrated that internal corrosion depth exceeds that of external corrosion. This study's data, focusing on large-diameter pipes, primarily involves samples from the upper part of the water supply chain, where water flows rapidly and in large volumes. These results suggest an erosive effect that compounds the corrosion issue. Additionally, this study found that overall corrosion depth in DIP was higher than in SP. SPs exhibited a high initial corrosion rate, which gradually decreased over time, whereas DIPs started with a lower corrosion rate that increased over time. The differing corrosion behaviors between SP and DIP can be attributed to their coating materials. Most DIPs examined were coated with cement mortar. At the same time, SPs typically had an epoxy resin coating, according to a study by Kim et al. (2018) on large-diameter pipes in the Republic of Korea, which aligns with the findings of this study, cement mortar coatings were estimated to have a lifespan of around 40 years. In contrast, epoxy resin coatings lasted about 60 years. Therefore, the deeper corrosion observed in DIPs relative to SPs is likely due to the shorter lifespan of their coating material.

For instance, in the case of SP under an average corrosion environment, combined internal and external corrosion depths were predicted to reach a maximum of 6 mm after 40 years of burial. The pipe thickness of a 1,500 mm diameter SP is approximately 15.0 mm (MOE 2010), indicating a local minimum pipe thickness of about 40% after 40 years of burial. Simply put, the pipe's tensile strength is proportionate to the pipe thickness, and the SF decreases to approximately 40% after around 40 years. This study utilized developed corrosion prediction models and applied stress derived from the pipe's environmental conditions to assess the structural safety of the pipeline.

Failure rate prediction models for SP and DIP were also developed using an ANN. Table 5 displays hyperparameter combinations and the performance of each model. All models exhibited a correlation coefficient of 0.90 or higher, indicating that well-developed models capable of accurately capturing the trends in actual data were achieved.

For SPs, the predicted failure rate typically shows a pattern where the rate increases sharply after a certain period. Despite some variations based on the conditions affecting failure, this rapid escalation in failure rate generally occurs after 20 years of burial. Conversely, DIPs exhibit an immediate rapid increase in the failure rate upon burial under failure-promoting conditions, with a tendency for this rate to rise continuously under other conditions.

Previously, the corrosion depth of DIP was greater than that of SP. However, the average failure rate was found to be lower for DIP compared to SP. DIP requires a thicker pipe thickness to achieve similar tensile strength even with the same pipe diameter. In Korea, for 1,000 mm pipes, the standard pipe thickness for SP is 10 mm, while for DIP, it is 16 mm (MOE 2010). This difference in basic pipe thickness is believed to explain the greater corrosion depth, but the failure rate is lower in DIP. Additionally, SP mainly uses welding, while DIP uses mechanical jointing. The worker's skill level often influences the construction status in welding, and it is suggested that the higher failure rate of SP, compared to DIP, may be linked to numerous failures, mainly leakages, occurring in buried SP during periods of insufficient construction technique in the past.

Based on the developed prediction models, a renewal investment optimization method developed in this study was applied in the target area in the Republic of Korea.

In Figure 7, Scenario A, representing the ‘do nothing’ approach, exhibited escalating maintenance costs amounting to 79.38 million USD over 40 years. This was due to the absence of renewal investment, leading to increased failure incidents and higher repair costs. This highlights that neglecting the renewal of aging pipes increases long-term costs and exposes water utilities to significant operational risks. On the other hand, Scenarios B, C, and D, where various renewal strategies were implemented, partially mitigated maintenance costs by reducing the frequency and severity of failures. However, these scenarios also demonstrated notable budget concentration in specific years, as large-scale pipe replacements were conducted during the planned replacement periods. This irregular budget allocation challenges water utilities regarding investment efficiency and financial planning.

Among the alternative plans, Scenario D emerged as the least costly option, with a total expenditure of 48.17 million USD over 40 years. In this scenario, pipe replacement was limited to segments with confirmed economic feasibility (BC > 1.0). The analysis revealed that replacements were primarily focused on larger-diameter pipes located at the top of the supply process, where failures caused substantial damage. Conversely, smaller-diameter pipes at the bottom of the supply chain were often neglected, resulting in minor but persistent damage. Although Scenario D minimized major damages at a lower cost, it was deemed less favorable from a water supply service perspective due to its potential impact on consumers.

Scenarios C and E utilized structural safety (SF) as a decision criterion, mandating replacement when the SF fell below 1.0. Scenario E, however, applied a budget constraint of 2,000 USD annually through DP, leading to consistent annual investment. This approach enabled water utilities to allocate resources efficiently over the 40-year period, avoiding the budget spikes observed in Scenario C. As a result, Scenario E achieved the highest IVI of 0.62 and the lowest average failure rate, making it the most balanced and sustainable plan among all scenarios.

In contrast to the irregular costs of other renewal methods, Scenario E effectively spread the investment across the entire analysis period, ensuring that water utilities could maintain high structural safety and asset value while minimizing risks to the pipe network. While Scenario E incurred slightly higher costs than economically focused plans like Scenario D, its ability to consistently maintain pipe safety and IVI underscores its stability and long-term viability.

Applying the developed method to the KJ conveyance pipe network demonstrates its effectiveness in achieving long-term sustainability. Specifically, the optimized Scenario E provides a balanced approach by adhering to an annual budget constraint of 2,000 USD while addressing economic efficiency and structural safety. By systematically renewing pipes based on their SFs and BC ratios, this method ensures consistent investment across the 40-year analysis period, avoiding the budgetary spikes observed in other scenarios. This approach provides multiple additional benefits compared to traditional methods, making it a more effective and sustainable solution for water utility management. First, the water utility can manage its pipes economically by minimizing life cycle costs while maintaining reliable service delivery. By adhering to a consistent annual investment plan, the utility can avoid unnecessary expenditure spikes and ensure financial stability over the long term. Second, this approach enhances structural safety within the pipe network. Systematically addressing pipes with critical safety risks in a timely manner significantly reduces the likelihood of catastrophic failures that could disrupt water supply services and incur substantial repair costs. Lastly, the prioritization strategy embedded in this method offers a clear and practical roadmap for renewal activities. This enables the water utility to allocate resources more effectively and plan operations more efficiently, ensuring that the most critical sections of the network are addressed first while maintaining overall network stability.

The increasing accumulation of aging pipes highlights the need for their effective management. In particular, in the case of conveyance pipes with large pipe diameters, more active management strategies are needed because the ripple effects in the event of failure are significant. This study introduces an optimization method for renewal investment plans based on DP. This approach simultaneously considers the structural safety of pipes and economic efficiency of renewal, areas traditionally addressed separately, and validates the methodology through a case study.

First, this study develops ANN-based models to predict pipe corrosion, assessing the structural safety of pipes. Failure rate prediction models are also developed to evaluate the economic efficiency of pipe renewal. Both models validated strong predictive capability, with correlation coefficients exceeding 0.85, indicating high accuracy in representing the collected data. DIP typically exhibited greater corrosion depth than SP, while SP showed a higher failure rate than DIP. This discrepancy was attributed to differences in pipe thickness and construction ability during periods of insufficient construction capacity.

Building on the developed corrosion and failure rate prediction models, this study evaluated the pipes' structural safety and the pipe renewal's economic efficiency. Subsequently, this study devised an optimization method to minimize life cycle costs while adhering to annual investment budget constraints, which was applied to a case study area. The renewal investment strategy formulated using the developed method proved more effective than the plan using a commonly used method, offering superior safety and economic advantages. The developed method achieved the highest IVI of 0.62, a metric for assessing renewal investment plan performance, and recorded the lowest average failure rate. This underscores its significant benefit in reducing risk within the conveyance pipe network. Moreover, the analysis revealed that leveraging annual budget constraints enables water utilities to manage their budgets efficiently, ensuring effective investment within predetermined limits each year.

Lastly, Scenario A demonstrated the economic benefits of pursuing the renewal of pipes by any means compared to abandoning them due to maintenance costs. This finding underscores the importance of devising proactive investment plans to renovate aging water infrastructure. Various frameworks have recently been developed to manage water infrastructures effectively within the asset management paradigm. The method introduced in this study can serve as a foundational technology for future asset management initiatives. This study presents limitations that necessitate further research to enhance the developed model. This study focused exclusively on the safety of conveyance pipes and the economic feasibility of renewal, overlooking water quality factors crucial for pipe renewal objectives. Given that distribution pipes also represent a significant area for investment, future studies could enhance the method by incorporating water quality considerations of the distribution network, thereby addressing current limitations.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.