1. Alireza Yazdani Post-Doctoral Research Associate Department of Civil & Environmental Engineering Rice University Presented at: SAMSI Uncertainty Quantification Transition Workshop May 22 nd, 2012

2. 2 SUSTAINABLE WATER SUPPLY MANAGEMENT SYSTEM PERFORMANCE EVALUATION UNCERTAINTY QUANTIFICATION NETWORK TOPOLOGY

3. 3 Water Distribution Systems (WDS) are large complex networks of multiple interdependent nodes (e.g. reservoirs, fittings, fire hydrants) joined by links (e.g. pipes, valves, pumps). Main system components: Source Treatment Transmission Storage Distribution A hypothetical network representation

4. The US Water infrastructure is old, fragile and inadequate in meeting the increasing demand for water. Last years Texas drought resulted in a spike in water main breaks (CBS local, Aug 2011). Existing centralized networks, suffer from high water age, bio-film growth, pressure loss and high energy consumption. There is currently an underinvestment (~ $108.6 Billion). 4 Source: (EPA, 2006 Committee on Public Water Supply Distribution Systems: Assessing and Reducing Risks, National Research Council, and 2009 Report Card for Americas Infrastructure)

5. 5 America's Infrastructure G.P.A. = D A = Exceptional B = Good C = Mediocre D = Poor F = Failing 2009 ASCE Report Card for Americas Infrastructure

6. 6 A sustainable Water Supply System is one that supplies anticipated demands over a sensible time horizon without degradation of the source of the supply or other elements of the systems environment.* Criteria: Reliability: adequate flow and pressure, availability of the physical components Water Quality: Acceptable water age and chemical contents Efficiency: leakage management, operational efficiency and environmental impacts Achieving sustainability requires integrated analysis and optimization of performance criteria while dealing with uncertainties in the data/model/natural environment * Water Distribution Systems (2011), D. Savic, J. Banyard (Eds.), ICE Press.

7. 7 Efficiency: what is the cost/impacts of getting water here? Adequacy (quality/quantity): How does water taste there? Is the pressure sufficient? Reliability: what if these pipes break together?! Reservoir and treatment facilities A slightly reconfigured EPANET representation of Colorado Springs WDS

8. 8 Reducible ( epistemic) uncertainty: Resulting from a lack of information in model about the system, typically reduced through inspection, measurement or improving the analogy between the abstract model and real system Irreducible (aleatoric) uncertainty: Natural randomness in a process, usually described by probabilistic approaches Image taken from: S. Fox (2011), Factors in ontological uncertainty related to ICT innovations, I. J. Manag. Proj. Busin, 4 (1), 137-149. Not to be absolutely certain is, I think, one of the essential things in rationality. Bertrand Russell

9. 9 Model (e): inability to represent true physics of the system and its behaviour Data (e): measurement error, inconsistent/inaccurate/inadequate data Operation (e): related to the system construction, design, equipments, deterioration, maintenance Natural (a): unpredictability of nature and its impacts on the system Determining the pipe size, tank diameter, network topology at design stage Placement of sensors/control valves to monitor water quality Prediction of the physical components failure rates and evaluating failure consequences Estimating water weekly/monthly/yearly water demand to support normal/peak consumption Assessing the impacts of climate/demographical changes on resources

10. 10 Pipe Break/Contaminant Ingress Source unavailable Reliability: how often the system fails (in quantity or quality terms). Vulnerability: how serious the consequences of the failure may be. Resiliency: how quickly the system recovers from failure. Reservoir Tank Reservoir WDS Performance is largely affected by network topology Uncertainty in system performance due to the unknown/unpredictable parameters may be reduced through studying topology.

11. 11 Centralized treatment/operation water quality deterioration cost of wastewater collection high energy loss Decentralized treatment shorter pipe lengths improved water quality? more efficient? Image from D. Kang, K. Lansey, Scenario-based Robust Optimization of Regional Water/Wastewater Infrastructure,doi:10.1061/(ASCE)WR.1943-5452.0000236

12. 12 MetricProxy for Spectral Graph Theory Fault-tolerance (design) Rate of contaminant spread Centrality measures Component criticality analysis Network vulnerability to random failures/targeted attacks Path length/distances Friction losses Design/Operation Cost Access between source and nodes Water residence time Loops Redundancy Reliability

13. Random networks: Random degree distribution (equal connectivity likelihood) Network equally vulnerable to failures/attacks (typical nodes) Examples: spatial networks (no hubs, large diameter) Small worlds: Gaussian or exponential degree distribution Large networks with low path lengths and high clustering Scale free networks: Scale-free networks/power law degree distribution Many low degree nodes with very few highly connected hubs Robust against random component failures yet fragile under targeted attacks on the hubs 13

14. 14 Image: Albert, Barabasi and Bonabeau, (2003), Scale-free Networks, Scientific American, 288, 50-59.

15. 15 Colorado Springs (CS), USA Richmond Yorkshire Water (RYW), UK City of Houston (COH), USA

16. 16 Metric Colorado Springs City of Houston Richmond Nodes17863926872 Links19945801957 Total pipe length (km)117.013166.1575.61 Average pipe length (m)187.12574.2633.09 Algebraic connectivity2.43 e-42.26 e-46.09 e-5 Average node degree2.232.962.19 Average path length27.2325.9451.44 Central-point dominance 0.420.340.56 Critical ratio of random breakdown 0.570.420.32 Graph diameter6972135 Maximum node degree494 Meshedness coefficient0.05860.2390.0495 Node (link) connectivity1 (1) Topological efficiency5.2 %2.4 %3.4 %

17. d=0.4 Demand-adjusted entropic degree (DAED)* combines topology and physics by incorporating the number of links attached to a node, the capacity of the link connections and the way they are distributed while taking into account the demand for water at each node. 17 i W1=1 i W1=0.5W2=0.5 i W3=0.6 W3=0.3 i W3=0.2 W3=0.3 * A. Yazdani, P. Jeffrey (2012), Water Resour. Res., doi:10.1029/2012WR011897, in press

18. 18 CSRYW

19. 19 Colorado Springs top three most important nodes IDDegreeDAEDNormalized DAED 1444 542.281 12293 354.360.65 13733 192.270.36 Richmonds top three most important nodes IDDegreeDAED Normalized DAED 1532 94.371 202 75.590.80 2192 64.380.68 CS RYW

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21. The analysis of WDS topology: Reduces model uncertainty and offers a computationally inexpensive and less data- dependent simplified approach Helps quantifying vaguely understood qualities such as redundancy, optimal- connectivity and fault-tolerance Supports development and comparison of the alternative design and operation (e.g. Decentralized) scenarios The UQ via studying interactions of system topology and performance (hydraulic reliability, energy use, water quality) provides theoretical support for finding sustainable solutions for water infrastructure systems planning and management (rehabilitation/design/expansion problems). Due to the WDS specifications, data and model uncertainties, and hydraulic complexities, advanced UQ techniques (e.g. spectral methods, multiple regression and survival analysis and non-parametric statistics) have a special place in the realistic analysis of WDS vulnerability/sustainability. 21

22. 22 Performance analysis and comparison of the centralized, decentralized and hybrid layouts in terms of water quantity and quality Analysis of historical failure data to develop component/system failure rate models serving reliability analysis Investigating the role of network topology (in the presence or absence of shut off valves) in facilitating mass transport/preventing the spread of contaminants within the system validated by the EPANET models

23. 23 Rice University Shell Centre for Sustainability SAMSI for the travel support Dr. Leonardo Duenas-Osorio and Dr. Qilin Li of Rice University Civil and Environmental Engineering