Effects of Pipe Roughness Uncertainty on Water Distribution Network Performance During its Operational Period

The design of new water distribution networks (WDNs) is an important social problem. Failures during an operational period provoke deficits in consumption nodes thus decreasing the performance of the network. WDN performance can be defined as the ability to sufficiently secure demand and desirable pressure in nodes based on changes in design parameters. This paper focuses on the evaluation of network performance during an operational period, taking into account pipe roughness uncertainty. A network analysis is performed by generating probabilistic series of pipe roughness using Monte Carlo simulation (MCS) in the operational period of the Two-loop WDN. Results show that an increase in pipe roughness uncertainty causes a decrease in network performance in the operational period. Furthermore, the network has a desirable efficiency only in the first 10 years. Thus, the proposed design methodology that considers the uncertainty of design variables is an effective procedure to evaluate network performance.     

A Superposed Model for the Pipe Failure Assessment of Water Distribution Networks and Uncertainty Analysis: A Case Study

Pipe failure often occurs in water distribution networks (WDNs) and results in high levels of water loss and socio-economic damage. Physical-based, statistical and data-driven models have been developed to estimate pipe failure rates (failures per km of pipe per year) to efficiently manage water losses from WDNs and to ensure safe operations. Due to the complexities of pipe failure patterns, we develop a superposed statistical model to depict the relationship between pipe failure rate and pipe age. The model’s level of uncertainty was then quantified by simulating pipe failures as Poisson numbers. Part of Beijing’s WDN is taken as a study case, and pipe failure data for a 4-year period, as well as pipe properties, are collected to develop the pipe failure model. The case study results show that the pipe failure rates vary with time in a non-monotonic manner and that the proposed model captures pipe failure behaviour with an R² value of 0.95. A 95% confidence interval of modelled pipe failures for each pipe age group is used to describe the uncertainty level of the model. We find that 88% of the observations fall under the 95% confidence interval. The established model could be applied to prioritize pipes with higher failure rates to optimize pipe replacement/rehabilitation strategies. Our uncertainty analysis of this model can help utility managers understand the model’s reliability and formulate reasonable WDN management plans.     

Calibration Model for Water Distribution Network Using Pressures Estimated by Artificial Neural Networks

The success of hydraulic simulation models of water distribution networks is associated with the ability of these models to represent real systems accurately. To achieve this, the calibration phase is essential. Current calibration methods are based on minimizing the error between measured and simulated values of pressure and flow. This minimization is based on a search of parameter values to be calibrated, including pipe roughness, nodal demand, and leakage flow. The resulting hydraulic problem contains several variables. In addition, a limited set of known monitored pressure and flow values creates an indeterminate problem with more variables than equations. Seeking to address the lack of monitored data for the calibration of Water Distribution Networks (WDNs), this paper uses a meta-model based on an Artificial Neural Network (ANN) to estimate pressure on all nodes of a network. The calibration of pipe roughness applies a metaheuristic search method called Particle Swarm Optimization (PSO) to minimize the objective function represented by the difference between simulated and forecasted pressure values. The proposed method is evaluated at steady state and over an extended period for a real District Metering Area (DMA), named Campos do Conde II, and the hypothetical network named C-town, which is used as a benchmark for calibration studies.     

Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs.     

Pipe Break Rate Assessment While Considering Physical and Operational Factors: A Methodology based on Global Positioning System and Data-Driven Techniques

An accurate prediction of pipes failure rate plays a substantial role in the management of Water Distribution Networks (WDNs). In this study, a field study was conducted to register pipes break and relevant causes in the WDN of Yazd City, Iran. In this way, 851 water pipes were incepted and localized by the Global Positioning System (GPS) apparatus. Then, 1033 failure cases were reported in the eight zones of understudy WDN during March-December 2014. Pipes break rate (BR_P) was calculated using the depth of pipe installation (h_P), number of failures (N_P), the pressure of water pipes in operation (P), and age of pipe (A_P). After completing a pipe break database, robust Artificial Intelligence models, namely Multivariate Adaptive Regression Spline (MARS), Gene-Expression Programming (GEP), and M5 Model Tree were employed to extract precise formulation for the pipes break rate estimation. Results of the proposed relationships demonstrated that the MARS model with Coefficient of Correlation (R) of 0.981 and Root Mean Square Error (RMSE) of 0.544 provided more satisfying efficiency than the M5 model (R?=?0.888 and RMSE?=?1.096). Furthermore, statistical results indicated that MARS and GEP models had comparatively at the same accuracy level. Explicit equations by Artificial Intelligence (AI) models were satisfactorily comparable with those obtained by literature review in terms of various conditions: physical, operational, and environmental factors and complexity of AI models. Through a probabilistic framework for the pipes break rate, the results of first-order reliability analysis indicated that the MARS technique had a highly satisfying performance when MARS-extracted-equation was assigned as a limit state function.

     

Evaluation of Reliability Indicators for WDNs with Demand-Driven and Pressure-Driven Models

Reliability of water distribution networks (WDNs) has received much attention in recent years due to progressive aging of infrastructures and climate change. Several reliability indicators, focusing on hydraulic aspects rather than water quality, have been proposed in literature. Reliability is generally assessed resorting to well established methods coupling hydraulic simulations and stochastic techniques that describe the WDNs hydraulic performance and component availability respectively. Two main algorithms are employed to simulate WDNs: the demand driven approach (DDA) that disregards the physical relationship between actual water demand and nodal pressure, and the pressure driven approach (PDA) that explicitly incorporates it. In this paper, we show how the choice of hydraulic solver may affect reliability indicators. We modify existing quantitative indicators at nodal and network level, and define novel indicators to consider water quality aspects. These indicators are evaluated for three example WDNs; discrepancies between results obtained with the two approaches depend on network size, feeding scheme and skeletonization. Results suggest to use with caution the DDA for reliability assessment at both local and global level.     

Optimal Design of Pipe Networks Accounting for Future Demands and Phased Expansion using Integrated Dynamic Programming and Differential Evolution Approach

The water distribution network (WDN) design comprises determining optimal pipe sizes to achieve minimum cost pipe network to meet the required demands and performance levels. However, with time, the water demand for any region changes due to population, migration, and lifestyles, so interventions need to be made to the existing WDNs. Therefore, the capacity expansion problem consists of determining the suitable interventions at various stages such that the required demands are met at minimum cost. The present study proposed a novel methodology for planning such interventions based on Dynamic Programming (DP) formulation and presented a combined Self-Adaptive Differential Evolution and DP (SADE-DP) methodology for solving the WDN expansion problems considering life cycle costs. The methodology is applied and tested on three benchmark WDNs, namely New York Tunnel (NYT), Two loop (TL), and Blacksburg (BLA) networks, and also for a real case study of the Badlapur WDN in Maharashtra, India. The proposed model solutions are validated by comparing them with other WDN expansion methods taken from the literature. The results indicate that the proposed SADE-DP approach is computationally efficient and provides cost-effective solutions by meeting desired performance levels at various stages, and can serve as a potential alternative for solving real-world WDN expansion problems.

     

Reliability-based Operation of Reservoirs Using Combined Monte Carlo Simulation Model and a Novel Nature-inspired Algorithm

One of the critical issues in surface water resources management is the optimal operation of dam reservoirs. In recent decades, meta-heuristics algorithms have gained attention as a powerful tool for finding the optimal program for the dam reservoir operation. Increasing demand due to population growth and lack of precipitation for reasons such as climate change has caused uncertainties in the affecting parameters on the planning of reservoirs, which invalidates the operational plans of these reservoirs. In this study, a novel optimization algorithm with the combination of genetic algorithm (GA) and multi-verse optimizer (MVO) called multi-verse genetic algorithm (MVGA) has been developed to solve the optimal dam reservoir operation issue under influence of the joint uncertainties of inflow, evaporation and demand. After validating the performance of MVGA by solving several benchmark functions, MVGA was used to find the optimal operation program of the Amirkabir Dam reservoir in 132 months, in both deterministic and probabilistic states. Minimizing the deficit between downstream demand and release from the reservoir during the operation period was considered as the objective function. Also, the limitations of the reservoir continuity equation, storage volume, and reservoir release equation were applied to the objective function. For modeling the effect of uncertainty, Monte Carlo simulation (MCS) is coupled to MVGA. The results of model implementations showed that the MVGA-MCS model with the best value of the objective function equal to 26 in the 1st rank and MVGA, MVO, and GA, with 15%, 34%, and 46% increase in the value of the objective function compared to the MVGA-MCS stood in the second to fourth ranks, respectively. Also, the results of the resiliency, and vulnerability indices of the reservoir operation showed that MVGA-MCS and MVGA models have better performance than other models.

     

EXPERIMENTAL STUDY OF FRICTION FACTOR FOR GROUNDWATER FLOW IN A SINGLE ROUGH FRACTURE

To study the relationships between the friction factor f and the flow type in a single rough fracture, the formulae of f for both unconfined and confined flows are deduced based on previous studies. The relationships between f and the Reynolds number (Re) for different relative roughnesses are investigated experimentally. The Moody-type diagram, based on the deduced formula of f, is also plotted and the hydraulic characteristics of the flow in a rough fracture are analyzed. Results show that the Moody-type diagram of the experiment has a similar distribution to that of the conventional Moody diagram. It is found that the value of f in the experiment is much smaller than that of the conventional Moody diagram and turbulent flow appears easier for rough fractures, which can be explained by the separation phenomenon in boundary layers. The critical Re ranging from 650 to 700 in rough fractures is concluded based on the experimental results. It also can be concluded that the friction factor f is related not only with the Re and the relative roughness but also with the absolute roughness.     

Enhancing Knowledge in Water Distribution Networks via Data Assimilation

This paper deals with uncertainty estimation and knowledge enhancement in water distribution networks (WDNs). A new three steps data assimilation approach is introduced, which in combination with multi-objective optimization, allows selecting effective and affordable monitoring networks. An innovative cascade of Ensemble Kalman Filters is used to assimilate the information deriving from sensors measuring pressure heads, flow in pipes and demands, with the objective of increasing knowledge while preserving at the same time the structural relationships among state variables. Selection of the most appropriate and economically affordable measurement network, is then based on the derivation of a Pareto front using the NSGA-II algorithm in conjunction with the data assimilation approach. The front is obtained by compromising between the overall sensors cost and the uncertainty reduction (or knowledge enhancement), which is expressed as a function of the Total Variance of state variables. The operational use of the proposed data assimilation approach as well as the effectiveness of the chosen observation network is also demonstrated by showing the reduction of uncertainty deriving from successive assimilations of real-time observations.     

Predicting Drought Magnitudes: A Parsimonious Model for Canadian Hydrological Droughts

A multiplicative relationship, drought magnitude (M) = drought intensity (I) × drought duration or length (L) is used as a basis for predicting the largest expected value of hydrological drought magnitude, E(M _T ) over a period of T-year (or month). The prediction of E(M _T ) is carried out in terms of the SHI (standardized hydrological index, tantamount to standard normal variate) sequences of the annual and monthly streamflow time series. The probability distribution function (pdf) of I (drought intensity) was assumed to follow a truncated normal. The drought length (L _c ) was taken as some characteristic duration of the drought period, which is expressible as a linear combination of the expected longest (extreme) duration, E(L _T ) and the mean duration, L _m of droughts and is estimated involving a parameter ø (range 0 to 1). The drought magnitude (deficit-sum, M) has been assumed to follow a gamma pdf, in view of the observed behavior of M. The model M = I × L has been invoked via two approximations, viz. Type-1 involves only mean of I and Type-2 involves both mean and variance of I through the theorem of extremes of random numbers of random variables. The E(L _T ) were obtained using the Markov chain (MC) model of an appropriate order, which turned out to be zero order Markov chain (MC-0) at the annual time scale. At the monthly time scale, the E(L _T ) was best represented by MC-0 for SHI sequences with low value of lag-1 autocorrelation (ρ?<?0.3) and first order Markov chain (MC-1) for SHI sequences with ρ?>?0.3. At low cutoff levels (q?≤?0.2), the trivial relationship E(M _T ) = E(I) × E(L _T ) i.e. without considerations of the extreme number theorem and the pdf of M yielded satisfactory results.     

WAVE DISSIPATING PERFORMANCE OF AIR BUBBLE BREAKWATERS WITH DIFFERENT LAYOUTS

The wave dissipating performance of air bubble breakwaters with different layouts is studied by experimental and numerical methods in this article. Based on the assumpation that the mixture of air and water is regarded as a variable density fluid, the mathematical model of the air bubble breakwater is built. The numerical simulation results are compared with the experimental data, which shows that the mathematical model is reasonable for the transmission coefficient Ct_m. The influencing factors are studied experimentally and numerically, including the incident wave height H_i, the incidentt wave period T, the air amount Q_m, the submerged pipe depth D and the single or double air discharging pipe structure. Some valuable conclusions are obtained for further research of the mechanism and practical applications of air bubble breakwaters.     

用分形几何理论研究圆管糙率及其实用意义

在已有紊流阻力定律与试验研究基础上,分析了当量糙率KS在计算紊流沿程阻力损失中的重要作用,以及我国水利工程沿程阻力损失计算和工程应用现状。以圆管内壁糙率为例,用分形几何理论研究了圆管糙率的分形特征,给出了圆管糙率分数维的数学模型和算例。论证了圆管糙率分数维和当量糙率KS的关系,分别讨论了管道纵、横向糙率分数维的计算方法,提供了将前人所建立的紊流阻力定律与试验结果直接用于工程实际的途径。     

Effect of bed roughness on grain-size distribution in an open channel flow

Grain-size distributions of suspended load were studied in a laboratory flume over five sediment beds having different values of bed roughness at three different flow velocities. The experiments had been performed to investigate the influence of bed roughness, flow velocity and suspension height on the grain-size distribution in suspension. This study focuses on the determination of the proportionality parameter β_n in suspension which is the ratio of sediment diffusion coefficient to the momentum diffusion coefficient of the nth grain-size class. An empirical equation for β_n has been proposed which is valid for a wide range of normalizing settling velocity of sediment particles and bed roughness. Also, the bed roughness effect is studied on the parameter β for total concentration in suspension and on the reference concentration, which is very important in suspension studies. The Rouse equation with modified β_n and β was surveyed to know the grain-size distribution and total concentration in suspension that agreed well when compared with the experimental data.     

A parametrical study on secondary flow in sharp open-channel bends: experiments and theoretical modelling

The dependence of curvature-induced secondary flow on the curvature ratio H/R (H is the average flow depth and R is the centreline radius of curvature), the Froude number Fr, and the dimensionless roughness coefficient C_f was systematically investigated in a series of 25 experiments in a laboratory flume. The investigated H/R values were (±0.005) 0.050, 0.073, 0.112 and 0.151, the Froude numbers were (±0.03) 0.10, 0.23, 0.32, 0.40 and 0.50, and roughness heights of the sediment bed were 0.002 m and 0.067 m. With width-to-depth ratios of 4.9 to 17.1, these experiments are more representative of small and medium-size rivers than the largest rivers on earth. Commonly used parameterizations for secondary flow predict the normalized magnitude to grow linearly with H/R, and to decrease with increasing bed roughness. This behaviour was only observed in mildly curved flows. The normalized magnitude was found to grow less than linearly with H/R in moderately curved flows, and to reach a maximum value in strongly curved flow. This confirms observations by Blanckaert (2009), who called this phenomenon the saturation of the secondary flow. He attributed the less than linear growth to nonlinear interactions between the primary and the secondary flows. For high values of H/R, secondary flow was found to be stronger over the very rough gravel bed than over the smoother sand bed. This is explained by the nonlinear interactions between the primary and secondary flows that are less pronounced over the rougher bed. The experiments did not reveal any dependence of the secondary flow on Fr. Predictions of the magnitude of the secondary flow with the nonlinear model of Blanckaert and de Vriend (2003, 2010) agreed very well with the experimental data over the entire range of investigated experimental conditions. Nonlinear effects are always important when the parameter $C_f^{-0.25}H/R$ is larger than an indicative value of 0.1, and negligible when this parameter is smaller than 0.05. These values allow a quantitative and objective distinction between mildly, moderately and sharply curved open-channel flow.     

A SECOND-ORDER MOMENT TURBULENCE MODEL FOR POWER LAW FLUID WITH PARTICLES

The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM ? θ model has better prediction result than the k f ? ε f?kp?εp?θ model. The USM ? θ model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.     

A Simplified Model for Predicting Drought Magnitudes: a Case of Streamflow Droughts in Canadian Prairies

The model for prediction of drought magnitudes is based on the multiplicative relationship: drought magnitude (M) = drought intensity (I) × drought duration (L), where I, L, and M are presumed to obey respectively the truncated normal probability distribution function (pdf), the geometric pdf, and the normal pdf. The multiplicative relationship is applied in the standardized domain of the streamflows, named as SHI (standardized hydrological index) sequences, which are treated equivalent to standard normal variates. The expected drought magnitude E(M _T ), i.e. the largest value of M over a sampling period of T-time units (T-year, T-month, and T-week) is predicted for hydrological droughts using streamflow data from Canadian prairies. By suitably amalgamating E(L _T ) with mean and variance of I in the extreme number theorem based relationship, the E(M _T ) is evaluated. Using Markov chain (MC), the E(L _T ) is estimated involving the geometric pdf of L. The Markov chains up to order one (MC-1) were found to be adequate in the proposed model for the annual to weekly time scales. For a given level of drought probability (q) and a sampling period T-time units; the evaluation of E(M _T ) requires only 3 parameters viz. lag-1 autocorrelation (ρ ₁ ), first order conditional probability (q _q , present instant being a drought given past instant was a drought) in SHI sequences and a parameter ø (value 0 to 1), which were estimated from historical data of streamflows. A major strength of the proposed model lies in the use of simple and widely familiar normal and geometric pdfs as its basic building blocks for the estimation of drought magnitudes.     

Excess Stormwater Quantification in Ungauged Watersheds Using an Event-Based Modified NRCS Model

Quantifying runoff from a storm event is a crucial part of rainfall-runoff model development. The objective of this study is to illustrate inconsistencies in the initial abstraction (I _a) and curve number (CN) in the Natural Resources Conservation Service (NRCS) model for ungauged steep slope watersheds. Five alternatives to the NRCS model were employed to estimate stormwater runoff in 39 forest-dominated mountainous watersheds. The change to the parameterization (slope-adjusted CN and I _a) leads to more efficient modified NRCS models. The model evaluations based on root mean square error (RMSE), Nash-Sutcliffe coefficient E, coefficient of determination (R ² ), and percent bias (PB) indicated that our proposed model with modified I _a, consistently performed better than the other four models and the original NRCS model, in reproducing the runoff. In addition to the quantitative statistical accuracy measures, the proposed I _a modification in the NRCS model showed very encouraging results in the scatter plots of the combined 1799 storm events, compared to other alternatives. This study’s findings support modifications to the CN and the I _a in the NRCS model for steep slope ungauged watersheds and suggest additional changes for more accurate runoff estimations.     

A comparative study of pseudo-static slope stability analysis using different design codes

Many researchers have developed new calculation methods to analyze seismic slope stability problems, but the conventional pseudo-static method is still widely used in engineering design due to its simplicity. Based on the Technical Code for Building Slope Engineering (GB 50330—2013) of China and the Guidelines for Evaluating and Mitigating Seismic Hazards in California (SP117), a comparative study on the pseudo-static method was performed. The results indicate that the largest difference between these two design codes lies in determination of the seismic equivalence reduction factor (f_eq). The GB 50330—2013 code specifies a single value for f_eq of 0.25. In SP117, numerous factors, such as magnitude and distance, are considered in determining f_eq. Two case studies show that the types of slope stability status evaluated by SP117 are in agreement with those evaluated by the seismic time-history stability analysis and Newmark displacement analysis. The factors of safety evaluated by SP117 can be used in practice for safe design. However, the factors of safety evaluated by GB 50330—2013 are risky for slope seismic design.     

Impacts on fish transported in tube fishways

Experimental data and numerical predictions of steady and unsteady flow in a 4 m high, 86 mm internal diameter tube fishway were compared quantitatively, and reflected expected uncertainties characteristic of the experiments and flow hydraulics. We then measured the response of a neutrally-buoyant fluid sensor and the behaviour of live fish transported vertically within the tube fishway. Ten repeat tests using the sensor and tests with seventy individual live fish demonstrated transport with 100% reliability. No ill effects were observed over a post-test monitoring period for two species of Australian native fish (Australian bass (Percalates novemaculeata) and Silver perch (Bidyanus bidyanus)) or as a function of size of the Silver perch that can be related to their passage through the fishway. There may have been temporary bruising of a few of the largest Silver perch tested. The largest Silver perch averaged 137 mm in length. The spatial distributions of the inert sensor and fish relative to the moving front during the transport process were quantified. Consequently, the volumes of water required during each operational cycle to ensure reliable delivery of fish over vertical distances less than 4 m were determined. The sensor measurements indicated negligible interactions with straight pipe walls but exposure to significant accelerations at sharp bends. Further experiments with live fish are required to quantify the possible adverse effects of alternative pipe transition designs on animals transported through them. Safe transport of fish up to a fish length/tube fishway delivery diameter ratio of 1.6 is demonstrated.