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CEE398,Lecture7Uncertainty,andwhattodoaboutit

CEE398/Fa13,Lecture7 1

SIT WITHSOMEONE

YOU DONT

KNOW

Quiz next

Thurs.

Whatsuptoday

Business

QuizThursdayQuesAons? HW3handedback

Technical

Summary:ClimateChange CombinaAonofUncertainAes nalysiswithUncertainty

CEE398/Fa13,Lecture7 2

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Wasteimpactsframework

forclimatechange1) Whatarethecarriersofharm?

CO2,CH4,N2O,HFCs(mainGHGs)&manyothers

2) Whattypeofharmisdone?Increaseinglobalaveragetemperature

ChangeinpaZernsofforcingandtemperature

lteringthesystemfasterthancapacitytoadapt

3)WhatacAviAesareresponsible?

IndustrialacAviAes,energyuse&agriculture4)Whatchangescanbeaccomplished?

ReduceemissionsrequiresinternaAonalagreement

CEE398/Fa13,Lecture7 3

Thesefactsareagreedbyalmosteveryone:

Thereisagreenhouseeffect.Watervaporisthemaingreenhousegas.CO2is

anotherone.

CO2concentraAonisincreasingduetoanthropogenicacAviAes.

Theeffectsofclimatechangewouldbeverydifferentineachworldregion.

CEE398/Fa13,Lecture7 4

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ThesequesAonsarenotwell

understood:Science

HowmuchwillthetemperatureoftheEarthrespond? KnownasClimatesensiAvity ffectedbyresponseofcloudsandwatervapor

Exactlyhowwillclimatechangeaffectindividualregions? HowwillclimatechangeaffectAppingpoints? Howwillclimatechangeaffectextremeevents,likehurricanes?Society

Canhumanshandletheeffectsofclimatechange? Shouldwedosomethingaboutclimatechange?

CEE398/Fa13,Lecture7 5

ComparingopAons*includinguncertainty

Threemethods

1) SimpleuncertaintypropagaAon(yourreading)2) Max/minvalues3) MonteCarlosimulaAon

CEE398/Fa13,Lecture7 6

* Comparing options is an inherent component ofdesign

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Possiblecomparisonoutcomes

CEE398/Fa13,Lecture7 7

Very different distributions dont overlap

Clear improvement

Very similar a lot of overlap

No clear improvement

Inconclusive

Improvement may occur, but

clouded by uncertainty

Review?

PropagaAonofuncertainty(summary)

1)CalculatedoutputxisafuncAonfofinput

variablesu,v,w:x=f(u,v,w)

2)Eachinputisuncertain:uhasuncertaintyu

3)Findtheuncertaintyinx

Assumpons:(i)usmallcomparedwithu,etc;

(ii)uncertainesinu,v,wuncorrelated

CEE398/Fa13,Lecture7 8

!x

2=

!f

!u

"

#$

%

&'

2

!u

2+

!f

!v

"

#$

%

&'

2

!v

2+

!f

!w

"

#$

%

&'

2

!w

2

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Onerealizaonofx

Ifu,v,wareexactlycentralvalue

CEE398/Fa13,Lecture7 9

Width of distribution comes from eithertrue uncertaintyorvariability

u

v

w

x

Anotherrealizaonofx

Inwhichu,v,warenotthecentralvalue

CEE398/Fa13,Lecture7 10

Width of distribution comes from eithertrue uncertaintyorvariability

u +!u

v +!v

w+!wx+!x

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DistribuAonparametersdescribeallrealizaAons

CEE398/Fa13,Lecture7 11

u +!u

v +!v

w+!wx+!x

u =1

Nui

i

!

!u

2=

1

N(u

i!u

i

" )2 =1

N#u

i

2

i

"

(Standard definitions ofthe mean and standard

deviation)

DerivaAon:PropagaAonofuncertainty

1) WriteTaylorseriesforonex2) Discardsecond-orderterms

Assumpon:(i)usmallcomparedwithu3) Expandproducts4) SumallrealizaAonsofxtogetdistribuAon5) Discardsomeoftheterms

Assumpon:(ii)uncertainesinu,v,wuncorrelated

CEE398/Fa13,Lecture7 12

!x

2=

!f

!u

"

#$

%

&'

2

!u

2+

!f

!v

"

#$

%

&'

2

!v

2+

!f

!w

"

#$

%

&'

2

!w

2

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Example1:Embodiedenergy

Howmuchenergyisembodiedinapassenger

automobile?

CEE398/Fa13,Lecture7 13

E = Mass x EE/kg

Example2:Embodiedenergytryagain

Howmuchenergyisembodiedinapassenger

automobile?

CEE398/Fa13,Lecture7 14

E = Mass1 x EE1/kg + Mass2 x EE2/kg +

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Example3:Embodiedenergyagain

Howmuchenergyisembodiedinapassenger

automobile?

CEE398/Fa13,Lecture7 15

E = Mass1 x EE1/kg + Mass2 x EE2/kg +

Example3:OperaAon

Howmuchenergyisconsumedbyapassenger

automobileduringitslifeAme?

CEE398/Fa13,Lecture7 16

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EmbodiedvsOperaAon

Forapassengervehicle,whichisgreater,

embodiedenergyoroperaAngenergy?

LookatthisquesAon3ways:

usingpreviousdata consideringvehiclesize usingmin/maxcomparisoninsteadof

propagateduncertainty

CEE398/Fa13,Lecture7 17

ReadingquesAon2

DescribeasituaAoninwhichknowinginput

uncertainAesiscriAcal.

CEE398/Fa13,Lecture7 18

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DistribuAonshapes

WeveimplicitlyassumedthatinputandoutputdistribuAonsarenormal.

Isthistrue? DoesitmaZer?

CEE398/Fa13,Lecture7 19

MonteCarloapproach

Usefulwhendistribuonsareoddlyshaped,or

x=f(u,v,w)isnon-linearorcomplex

1) Chooseeachinputparameter(u,v,w)byrandomsampling*

2) Calculateoutput(x)andstoreit3) Gobacktostep(1)unAlsaAsfied(N>30)4) StoredresultsgivedistribuAonofxCEE398/Fa13,Lecture7 20* More on this next.

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Randomsamplingofinputparameters

DeterminecumulaAveprobabilitydensityfuncAon Choosevaluebetween0and1usinguniform

probabilitydistribuAonfoundony-axis

Locatevalueofinputat

corresponding

valueonx-axis

CEE398/Fa13,Lecture7 21

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

Die face value

Cum

ulativeprobability

Inputparameters(2)

CEE398/Fa13,Lecture7 22

Springfield, IL

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Wind speed (m/s)

Cumulativefrequency

Worksforfunny-shapeddistribuons,too

Determinecdf Uniformvalue

between0and1

Locatecorrespondingvalueonx-axis

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UlAmategoal

WhetheryouuseuncertaintypropagaAon,min-maxcomparison,orMonteCarlo

GoaliscomparingtwodistribuonstoassesstwoopAonsnotjustthecentralvalue

Result:Whichisgreater?Whichismoreimportant?Whatismyconfidenceinthat

statement?

CEE398/Fa13,Lecture7 23

Whoaretheexperts?

ObtaininginputdistribuAonsExpertsineachfieldgivecentralvaluesand

uncertainAes

StaAsAcians

CEE398/Fa13,Lecture7 24