Visualisation and interaction for design

Introduction Process Integration Water distribution Summary

Visualisation and interaction for design

Professor Eric S Fraga

Department of Chemical EngineeringUCL (University College London)

ECOSSE Retrospective SymposiumEdinburgh

17 April 2009

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c©2009, All rights reserved.


Process design

Process design should be informed by robust optimisation withconfidence in results. But...

complex non-linear, non-convex,discontinuous & noisy models,

combinatorial search space,

small, possibly non-convex, feasibleregions, and

ill- or un-defined objective functionand constraint equations outsidefeasible regions.

600

700

800

900

1000

1100

1200

1300

1400

1500

0 5 10 15 20 25 30 35

Cos

t (k$

/yr)

Pressure (atm)

Cost versus Pressure

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The simplest things give me ideas.

Joan Miro

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Visualisation and interaction

Computer based tools for design and optimization areintended for use by non-experts.

Visual representations critical for ease of use.

Interaction can enable engineer to apply own intuition.

Strategy is to combine data analytics, visualisation, androbust (hybrid) optimisation.

Applications in energy, water, carbon capture, sustainability,and control.

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Heat-integrated process design

Task:

Identify potentialintegrations for givenconfiguration.

Enable processmodification forbetter integration.

Help engineer identifydesign alternatives.

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To simplify complications is the first essential ofsuccess.

George Earle Buckle

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Visual representation

For a given process configuration, we can display the hot andcold streams visually and support interaction, where

x-axis for position independentduties,

y -axis for temperature, and

hot stream overlapping coldstream indicates heat integration.

Allow user to manipulate process by moving streams (the tailwagging dog approach): streams can be moved horizontally fordifferent integrations and moved vertically or stretchedhorizontally to change underlying unit designs.

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HEN design algorithm

A graphical view ofprocess heat requirementsdefines left and rightend-points for each hotand cold stream in theprocess:

{(xa,i , ya,i)}

{(xb,i , yb,i)}

i = 1, . . . , ns andx , y ∈ Z+.

1 Define list of intervals

I ←ns⋃1

{{xa,i} ∪ {xb,i}}

2 For each interval [Ij , Ij+1]:

1 Generate list of active streams, A.2 Sort A from top to bottom using yb values.3 Generate match for each hot stream

immediately above cold stream in A.4 Generate utility match for all other

streams.

3 Coalesce adjacent similar matches.

4 Design exchanger for each match.

5 Cost all exchangers and utility use.

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Demonstration

www ESF, Patel & Rowe (2001). ChERD 79(7):765–776

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http://www.homepages.ucl.ac.uk/~ucecesf/images/qt-visualisation-animated.gif


Water distribution networks

We wish to design the pipe network for water distribution for agiven configuration with the aim of meeting water demandwith redundancy in the network. A small motivating problem:

7 nodes

8 pipes

1 reservoir

no pumps

Alperovits & Shamir (1977), Water Resource Research 13(6):885-900

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The design problemGiven

network layout: connectivity, length (Lk), set of discrete pipediameters, pipe cost;

node demands, Dn; and,

minimum head requirements, Hminn .

Determine

diameter of each pipe, dk , chosen from the set of discretediameters;

flow amount and direction, Qk ; and,

head (pressure) at each node, Hn

so as to minimise total network cost.

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The model

min∑

k

∑m

CmLkykm

subject to: ∑k∈In

Qk −∑k∈On

Qk = Dn

∆Hk = Hn∈Ik − Hn∈Ok

∆Hk = w

(Qk

CHW

)βLk

∑m

d−γm ykm

Hn ≥ Hminn + En∑

m

ykm = 1

Indices: k , pipes/connections, n, nodes, and m, pipediameters.

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Direct optimization

Solved minlp in gams, using dicopt with the cplex milpsolver and a variety of nlp solvers:

Initial Solution (103 $)

Configuration conopt2 conopt3 minos minos5

None 659 655 444 Fails

All flows = 100 441 441 452 452

Initialization affects success of the nlp solvers.

Consider visual and interactive tool for initialization ofsubsequent mathematical programming method: hybridapproach.

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Simplicity and complexity need each other.

John Maeda

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Discrete optimization

Use of visualization requires mapping from continuous todiscrete space.

Mapping converts MINLP to discreteprogramming model ...

... but equality constraints cannot besatisfied in discrete space.

So we use interval analysis to identifysolutions which are close to feasible indiscrete space.

The discrete model is solved either by the engineer throughinteraction or using an embedded stochastic optimisationprocedure.

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Interval arithmetic

Changes to model given that node heads are now intervals:

∆Hk = Hn∈Ik − Hn∈Ok

Qk =

(∆Hk

w Lk

Cβdγk

) 1β

0 ∈∑k∈In

Qk −∑k∈On

Qk − Dn

where indicates an interval value.

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Demonstration

www ESF & Papageorgiou (2007), Optimization and Its Applications, Springer, 4:311-332.

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http://www.homepages.ucl.ac.uk/~ucecesf/images/water-animation.gif


Hybrid procedure results

Initial Solution (103 $)

Configuration conopt2 conopt3 minos minos5

None 659 655 444 Fails

All flows = 100 441 441 452 452

Hybrid 419 419 423 419

Behaviour of nlp solvers is more consistent.

The global optimum is found in 3 of the cases.

Solutions obtained are better in all cases.

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Summary

To simplify complications is the first essential ofsuccess.

George Earle Buckle

But...

Everything should be made as simple as possible, butnot simpler.

Albert Einstein

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Acknowledgements

The following have contributed to the work presented here:

Dr Lazaros Papageorgiou, UCLMs Rupal Patel, UCL

Dr Glenn Rowe, Dundee

and the ECOSSE group is to blame for my working in thisfield!

http://www.homepages.ucl.ac.uk/~ucecesf/research.html

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Visualisation and interaction for design

Design

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