Integrated Empirical Stochastic Modeling for Economic Design of Branched Water Pipeline Networks

Efficient and economical design of pumping water supply systems remains challenging due to uncertainties in pipe sizing. Conventional methods that balance capital and energy costs often oversimplify design factors, leading to over- or under-design. This study presents an integrated framework combining empirical modeling, hydraulic simulation, and probabilistic analysis to improve pipe sizing in branch networks. An empirical discharge–diameter relationship, formulated using key global design parameters, including the population projection ratio, pump efficiency, and pipe cost variation, along with logarithmic and diurnal correction, predicts pipe sizes within ±6% error, validated using the root mean square error, mean absolute error, and adjusted R2 metrics. The multistage economic pipe-sizing (EcoPS) algorithm iteratively refines diameters along critical and noncritical paths while ensuring hydraulic grade line (HGL) compliance and minimizing system costs. The framework demonstrates four key strengths. First, it enables cost optimization; case studies demonstrate a 30.17% increase in pipe costs, 49.31% reduction in energy costs, and 17.83% decrease in total costs, confirming economic viability. Second, it enhances operational flexibility by partially shutting down elevated service reservoirs rather than full service interruption. Third, ensures predictive scalability: Monte Carlo simulations combined with the multistage EcoPS algorithm are applied to field statistics to produce HGL envelopes that closely align with deterministic design outputs, validating reliability under data-sparse conditions. Finally, a least-squares projection–based diameter redistribution (LSP-BDR) module is applied to filter unrealistic diameter outliers and derive interpretable weight spectra, supporting robust precost estimation and planning. Together, the Monte Carlo analysis and LSP-BDR postprocessing enhance generalization capability. Consequently, stochastic outcomes from one network are effectively transferred to hydraulically similar systems with only ∼3.5% deviation in total cost, validating cross-system reliability and scalability. Overall, these components form a unified and scalable framework capable of delivering resilient, cost-effective water supply networks, even in contexts with limited or uncertain field data.