Quantifying Uncertainty to Support Sustainable Planning and Management of

Water Supply Infrastructure

Alireza Yazdani

Post-Doctoral Research AssociateDepartment of Civil & Environmental Engineering

Rice University

Presented at:SAMSI Uncertainty Quantification Transition Workshop

May 22nd, 2012

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SUSTAINABLE WATER SUPPLY MANAGEMENT

SYSTEM PERFORMANCE EVALUATION

UNCERTAINTY QUANTIFICATION

NETWORK TOPOLOGY

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Water Supply Infrastructure

• 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

• The US Water infrastructure is old, fragile and inadequate in meeting the increasing demand for water.

• Last year’s 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

The problem

Source: (EPA, 2006 Committee on Public Water Supply Distribution Systems: Assessing and Reducing Risks, National Research Council, and 2009 Report Card for America’s Infrastructure)

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Aviation DBridges C Dams DDrinking Water D-Energy D+Hazardous Waste DInland Waterways D-Levees D-Public Parks & Recreation C-Rail C-Roads D-School DSolid Waste C+Transit DWastewater D-

America's Infrastructure G.P.A. = D

A = Exceptional B = GoodC = MediocreD = Poor F = Failing

2009 ASCE Report Card for America’s Infrastructure

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Sustainability

• 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 element’s of the system’s 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.

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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

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Uncertainty and Decision Making• 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

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Examples from Water Supply Engineering

• 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

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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.

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• 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

The Need and Practicality

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Network measurements

Metric Proxy 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

• 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

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Network topology models

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

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Case studiesColorado Springs (CS), USA

Richmond Yorkshire Water (RYW), UK

City of Houston (COH), USA

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Case studies (cont.)Metric Colorado

SpringsCity of

HoustonRichmon

d

Nodes 1786 3926 872Links 1994 5801 957Total pipe length (km) 117.01 3166.15 75.61

Average pipe length (m) 187.12 574.2 633.09

Algebraic connectivity 2.43 e-4 2.26 e-4 6.09 e-5

Average node degree 2.23 2.96 2.19

Average path length 27.23 25.94 51.44

Central-point dominance 0.42 0.34 0.56

Critical ratio of random breakdown 0.57 0.42 0.32

Graph diameter 69 72 135

Maximum node degree 4 9 4

Meshedness coefficient 0.0586 0.239 0.0495

Node (link) connectivity 1 (1) 1 (1) 1 (1)

Topological efficiency 5.2 % 2.4 % 3.4 %

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.

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Generalized connectivity(an example of reducing model uncertainty at the fine scales)

i

W1=1

i

W1=0.5 W2=0.5

i

W3=0.6

W3=0.3

W3=0.3

i

W3=0.2

W3=0.3 W3=0.3

* A. Yazdani, P. Jeffrey (2012), Water Resour. Res., doi:10.1029/2012WR011897, in press

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Generalized connectivity (cont.)

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Colorado Springs’ top three most important nodes

ID Degree DAED Normalized DAED

144 4 542.28 1

1229 3 354.36 0.65

1373 3 192.27 0.36

Richmond’s top three most important nodes

ID Degree DAED Normalized DAED

153 2 94.37 1

20 2 75.59 0.80

219 2 64.38 0.68

Generalized connectivity (cont.)

CS RYW

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Generalized connectivity (a WDS specific alternative for degree distribution)

0.0

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0%

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100%

Richmond

Colorado Springs

Normalized DAED

Pr {

> f

}

• 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.

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Summary and Conclusions

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Ongoing and future work

• 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

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Acknowledgements

• 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