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OutlineOutline

Soft Computing: ANFIS & Fuzzy ClusteringSoft Computing: ANFIS & Fuzzy Clustering

Fuzzy Rules & ANFISFuzzy Rules & ANFIS Fuzzy ClusteringFuzzy ClusteringTime Series of Sun Spot Numbers, RainfallTime Series of Sun Spot Numbers, Rainfall

& Water Level === Weather/Climate& Water Level === Weather/ClimateForecastingForecasting

System DynamicsSystem Dynamics ConclusionConclusion

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Sugeno Fuzzy RulesSugeno Fuzzy Rules

For x is AFor x is Aii and y is Band y is Bjj then z is pthen z is pii*x +*x +qqjj*y + r*y + rijij

Learning Rules :Learning Rules :

v_k = -v_k = - e_tot/v_ke_tot/v_k

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Adaptive Neuro FuzzyAdaptive Neuro Fuzzy

Inference SystemInference System

A1

A2

B2

B1 N

N

layer 1

layer 2

layer 3

layer 4

layer 5

x y

1w

2w

1w

2w

x y

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ANFISANFIS

Layer 1Layer 1 ::

xx andand yy areare inputinput ofofode -i anode -i andd O1,iO1,i isismembership function ofmembership function offuzzyfuzzysetsetA=(A1,A2A=(A1,A2) and B=() and B=(B1B1 ,,B2B2 )) withwithmembership functionmembership function AA isis ::

ai,bi,ai,bi, andand cici areare parameterparameterss Layer 2 :Layer 2 : output as the product ofoutput as the product of

input membership functionsinput membership functions ::

2

1,

1,

( ), 1, 2,

( ), 3, 4,

i

i

i A

i B

O x for i or

O y for i

b2

i

i

A

a

cx1

1)x(

+

=

2,1i)y()x(wOii BA1i,2

===

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Layer 3Layer 3 inin node -i :node -i :

Layer 4 :Layer 4 : Node -iNode -i isisadaptiadaptiveve nodenode withwith

funfunctionction node :node :

2,1i,ww

wwO

21

ii

i,3

=+

==

)ryqxp(wfwO iiiiiii,4 ++==

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ANFISANFIS

Layer 5 :Layer 5 : finalfinal output :output :

5

i i

ii i

i i

i

w f

O w f w

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Solar activities &Solar activities & ClimateClimate

Microphysics Cumulus

Solar and its activities PBL

Earth Surface

surface T,Qv,Wind

Surface FluxSH,LH

IncomingSW,LWSurface

Emisi/albedo

Cloud Fraction

Cloud Effects

Cloud detrainment

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S.Duhau : Temp vs SolarS.Duhau : Temp vs Solar

ActivitiesActivities

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S. Duhau : Temp AnomaliesS. Duhau : Temp Anomalies

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SSN, AA Index & CMESSN, AA Index & CME

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Cosmic ray & SunspotCosmic ray & Sunspot

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Elnino-Lanina Years

0,00

50,00

100,00

150,00

200,00

1948

1950

1952

1954

1956

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

Years

SunspotN

umber

sspot

L E L E L E E L E L E E L E L L E L E L E L E

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Pontianak Region

Correlation Sunspot vs Precip =0.88

0.00

50.00

100.00

150.00

200.00

1948

1951

1954

1957

1960

1963

1966

1969

1972

1975

1978

1981

1984

1987

1990

1993

1996

1999

2002

Years

Sunspot/P

recip

-50.00

0.00

50.00100.00

150.00

200.00

ave-sunspot ave-precip

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Jaya Pura Region

0.00

50.00

100.00

150.00

200.00

250.00

300.00350.00

1948

1951

1954

1957

1960

1963

1966

1969

1972

1975

1978

1981

1984

1987

1990

1993

1996

1999

2002

Years

mm/

month

0.00

50.00

100.00

150.00

200.00

Avg precip sspot

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Jabodetabek

0.00

50.00

100.00

150.00

200.00250.00

1948

1951

1954

1957

1960

1963

1966

1969

1972

1975

1978

1981

1984

1987

1990

1993

1996

1999

2002

Years

mm/m

onth

0.00

50.00

100.00

150.00

200.00

Avg Precip Avg-sspot

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Fuzzy c-means AlgorithmFuzzy c-means Algorithm

Fix c (2Fix c (2cc n) and select a value for parametern) and select a value for parameterm, initialize the partition matrix Um, initialize the partition matrix U(0)(0),,membership functions and the centers . Eachmembership functions and the centers . Each

step in this algorithm will labeled r, wherestep in this algorithm will labeled r, where

r=0,1,2,..r=0,1,2,..

Repeat updating the partition matrix forRepeat updating the partition matrix for rrthth

step,Ustep,U(r)(r)

untiluntil

+ )()1( rr UU

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Calculate the new membershipCalculate the new membershipfunctionsfunctions

1)1'/(2

1 )(

)(

)1(

==+

m

c

j drjk

dr

ikrik

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set r=r+1set r=r+1 Calculate the new c centers :Calculate the new c centers :

=

== n

kmik

n

k kjxm

ik

ij

v

1'

1

.'

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Fuzzy ClusteringFuzzy Clustering

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Long Time Prediction Based onLong Time Prediction Based on

Sunspot NumberSunspot NumberANFIS PREDICTION

0

50

100

150

200

1948

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000

2004

2008

2012

Years

NumbersSun

sp

ANFIS Prediction Obs. Sunsspot

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ConclusionsConclusions

ANFIS and Fuzzy Clustering can beANFIS and Fuzzy Clustering can beused in prediction of climate inused in prediction of climate in

IndonesiaIndonesia

Solar Activity is the main factor thatSolar Activity is the main factor that

determined climate in Indonesiadetermined climate in Indonesia

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