07n uncertainty
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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
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