Outline

1. The University of Adelaide, AustraliaSchool of Civil, Environmental & Mining EngineeringWater Systems and Infrastructure Modelling & Management Group (WaterSIMM) Using Genetic Algorithms to Optimise Network Design and System Operation Including Consideration of SustainabilityProfessor Angus SimpsonVictorian Modelling Group24 March 2010

2. Outline • Simulation of water distribution systems • Various formulations of equations • Todini and Pilati solution method • Genetic algorithm optimisation of water distribution system networks • Genetic algorithms for optimising operations of pumping systems • Optimising for sustainability

3. My research interests • Optimisation of the design and operation of water distribution systems using genetic algorithms [including sustainability considerations (GHGs)] • Monitoring health and assessing condition of pipes non-invasively in water distribution systems using small controlled water hammer events

4. My research interests • Steady state computer simulation analysis of water distribution systems - improving solvers and modelling of PRVs and FCVs • Water hammer modelling in pipelines

5. The research team • Total of 14 • 9 academics (local and overseas) • 1 Research Post Doc. • 4 PhDs

6. The research team - academics • Prof. Angus Simpson • Prof. Martin Lambert (condition assessment and genetic algorithms) • Prof. Holger Maier (genetic algorithms and sustainability) • Dr. Sylvan Elhay – School of Computer Science, The University of Adelaide (steady state solution of pipe networks) • Prof. Lang White – School of Electrical and Electronic Engineering, The University of Adelaide (condition assessment)

7. International collaboration • Professor Caren Tischendorf – Head of Dept. of Mathematics and Computer Science, University of Cologne, Germany (steady state solution of pipe networks) • Dr. Jochen Deuerlein – 3S Consult, Germany (steady state solution of pipe networks, correct modelling of PRVs, FCVs in water networks) – ex-University of Karlsruhe • Dr. Arris Tijsseling – University of Eindhoven, The Netherlands (condition assessment) • Prof. Wil Schilders – University of Eindhoven, The Netherlands (speeding up solution of nonlinear steady state pipe network equations)

8. Components in a Water Distribution System

9. Simulation of water distribution systems • Solution of a set on non-linear equations for • flow (Q) and • pressure (head or hydraulic grade line – H) • EPANET uses Todini and Pilati (1987) method – very fast • There are many sophisticated commercially available software packages

10. Assumptions • Fixed demands – assumed to be not pressure dependent, for example - 100 houses aggregated to a node • Various water demand loadings cases • Peak hour (hottest day in summer) • Peak day (extended period simulation usually over 24 hours to check tanks do not run empty) • Fire demand loading cases • Pipe breakage cases

11. Decisions to be made • Diameters and locations of pipes • Location of pumps • Locations and setting of valves (PRVs, FCVs) • Locations and elevations of tanks • Operation of pumps – off-peak electricity rates • Minimising carbon footprint • Reliability considerations

12. Design objectives • For the economic cost component minimise sum of • Capital cost of the water distribution system(say for a 100 year life) • Present value of pump replacement/refurbishment(every 20 years) • Present value of pump operating costs (100 years)

13. C: Payment/cost on a given future date t = Number of time periods i = Discount rate Accounting for Time • Present value analysis (PVA) • Usually the discount rate i is selected to be cost of capital 6 to 8% • For social projects, such as WDSs, a social discount rate should be used, for example, i = 1.4% (intergenerational equity)

14. Design objectives • Satisfy design criteria – for example • Minimum/maximum allowable pressures • Maximum allowable velocities • Tanks must not empty

15. Trial and error approach • User has to choose - diameters of pipes, locations of tanks, pumps, and PRVs • Engineering judgment and experience • Run simulation model for demand load cases • Check design criteria and compute cost • Adjust sizes of elements in response to pressures • Rerun simulation model

16. New York Tunnels problem

17. A very very large search space size • Any one of the 21 existing pipes could be duplicated • Choose from 16 allowable pipe sizes to meet demands • Search space size = 1.43 x 1021 • Eliminate 99.99% of possible solutions by engineering experience (leaves 1.43 x 1017)

18. A very very large search space size • At 10,000 evaluations per second – can compute 3.15 x 1011 per year • It will take 454,630 years to fully enumerate 0.01% of the total search space (only for 21 decision variables)

19. A typical simple water distribution system

20. Simulation – Solving for The Unknowns • Only consider systems with pipes and reservoirs • The unknown flow vector (10 pipes in examples) • The unknown head vector (7 nodes in example) (gives pressures)

21. A total of 17 unknowns Qs and Hs

22. Continuity Equation of Flow at a Junction • Flow In = Flow Out + Demand (or Withdrawal Discharge) • where • Qj = flow in pipe j (m3/s or ft3/s) • NPJi = number of pipes attached to node i • DMi = demand at the node i (m3/s or ft3/s) • NJ = total number of nodes in the water distribution system (excluding fixed grade nodessuch as reservoirs)

23. Pipe Head Loss Equations in Terms of Nodal Heads • where • = nodal head at node i in the water distribution system (m or ft) • rj = resistance coefficient for the pipe j depending on the head loss relationship (for example, Darcy–Weisbach or Hazen–Williams) • Qj = flow in pipe j (m3/s or ft3/s) • n = exponent of the flow in the head loss equation (Darcy–Weisbach n = 2 or Hazen–Williams n = 1.852)

24. Four different non-linear formulations • #1 Q-Equations • #2 H-Equations • #3 LF- Equations (Loop Flow Equations) • #4 Todini and Pilati H-Q Equations

25. #1 - The Q-equations formulation (10 unknowns)

26. The Q-equations (10 unknowns)

27. The Q-equations (Newton iterative solution technique)

28. #4 -Todini and Pilati Q-H formulation • Define topology matrices • Develop block form of equations • Use an analytic inverse of block matrices to reduce matrix size from 17 unknowns to 7 unknowns (same as unknown heads H) • Fast algorithm

29. Todini and Pilati Q-H formulation • Unknowns

30. Todini and Pilati Q-H formulation - Define topology matrices

31. Todini and Pilati Q-H formulation - Define topology matrices

32. Todini and Pilati Q-H formulation - continuity at nodes

33. Todini and Pilati Q-H formulation – head loss equations for pipes Note that later on theinverse of this matrix will give problems for zero flows

34. Todini and Pilati Q-H formulation – head loss equations for pipes

35. Todini and Pilati Q-H formulation–two sets of equations

36. The Todini and Pilati equations

37. Improving solution speed • Making solution algorithms more robust – zero flows cause Todini and Pilati method to fail – a regularization method has been developed to control the condition number • An improved convergence criterion for stopping has been developed Research Issues

38. Decomposing networks into trees, blocks and bridges to speed up analysis • Growing typical networks that have correct mix of loops, links and junctions Research Issues

39. GENETIC ALGORITHMS FOR OPTIMISATION OF WATER DISTRIBUTION SYSTEMS

40. Types of Evolutionary Algorithms • Genetic algorithms (Holland 1976; Goldberg 1989) • Ant Colony Optimisation (ACO) • Tabu search • Simulated annealing • Particle swarm optimisation (PSO) • Evolutionary strategy (Germany)

41. History of genetic algorithms applied to water distribution systems • Pioneered at the University of Adelaide by Laurie Murphy under my supervision in an honours project in 1990 and a PhD starting in 1991 • Initial focus was on the optimisation of the design of water distribution systems • A spinoff company of Optimatics Pty Ltd formed by University of Adelaide in 1996 – operates in Australia, NZ, USA and UK (employs 20 people) • Research focus is now on optimising operations and accounting for multiple objectives (sustainability, reliability)

42. Genetic algorithm optimisation • Population orientated technique (select a population size of say 500) • Based on mechanisms of natural selection and genetics • Selection, crossover and mutation operators produce new generations of designs • Fitness of strings drives process • Uses EPANET type simulation model to assess performance of all trial water distribution networks in each generation

43. Creating a string from sub-strings - an example BINARY CODING

44. Chromosome of decision variables • Choice tables are required for each decision variable Existing pipe [3] (binary) 00 = no change, e = 2.5 mm 01 = clean/line, e = 0.3 mm 10 = duplicate 306 mm 11 = close the pipe Chromosome

45. Model Operation GA OPTIMISATION MODEL Configuration of water distribution and performance passes back and forth HYDRAULIC SIMULATION MODEL Optimisation-Simulation Model Link

46. Simulate hydraulics of water distribution system • Decode each string using the choice tables • Run a computer simulation model • Simulate demand loading cases consecutively – peak hour, fire, extended period simulation • Record any violation of constraints (e.g. pressures too low, velocities too high)

47. Choices for the decision variables

48. Total cost and corresponding fitness of the string • Total cost is the: example • Real cost of the water distribution system design PLUS • A penalty pseudo-cost (or costs) if the constraint(s) are not met • For example =K*Maximum pressure deficitwhere K=$50,000 per metre • Fitness is often taken as the inverse of the total cost

49. Steps in a genetic algorithm optimisation • Select a population size (e.g. N=100 or N=500) • Select a reproduction or selection operator • Select a probability of crossover (Pc) • Select a probability of mutation (Pm)

50. A Simple Genetic Algorithm This Generation N=500 Selection Crossover & Mutation Mating Pool N=500 The Next Generation