SLIDE 1
Determining the Model Order
- f Nonlinear
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Determining the Model Order of Nonlinear Input-Output Systems by - - PowerPoint PPT Presentation
Determining the Model Order of Nonlinear Input-Output Systems by - - PowerPoint PPT Presentation
Determining the Model Order of Nonlinear Input-Output Systems by Fuzzy Clustering Balzs Feil, Jnos Abonyi and Ferenc Szeifert University of Veszprm, Department of Process Engineering www.fmt.vein.hu/ softcomp 2/10 Overview
SLIDE 2
SLIDE 3
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Model Order Selection
[ ]
) ( )] ( ),..., ( ), ( ),..., 2 ( ), ( [ ) (
,
t G m t u t u l t y t y t y G t y
m l
ψ τ τ τ τ τ = − − − − − =
?
u y
?
System
SLIDE 4
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The basic idea of FNN
Geometrical view Finds the nearest neighbors of all data Calculates the ratio of the bad neighbors Critical step: what are the bad neighbors?
1 variable 2 variables 3 variables
SLIDE 5
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The FNN algorithm
Find the nearest neighbor Find the nearest neighbor what is the relative distance what is the relative distance
- f the related outputs
- f the related outputs
New data New data form all data form all data Calculate the ratio of Calculate the ratio of the the bad neighbors bad neighbors Increase the Increase the dimension dimension
2 , , min
) ( ) ( j k D
m l m l j
ψ ψ − =
≤ − −
2 , ,
) ( ) ( ) ( ) ( j k j y k y
m l m l
ψ ψ
R
How can we define R to get good results?
SLIDE 6
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Cluster based determination of R
Gath-Geva clustering Cluster prototype (center, covariance matrix) Extraction of the parameters of local linear models
x y
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The proposed algorithm
Identification data in the increased dimensional space Identification data in the increased dimensional space Selected data and its Selected data and its nearest neighbor nearest neighbor R R Bad or good neighbors Bad or good neighbors New data New data Calculation of the ratio Calculation of the ratio
- f the bad neighbors
- f the bad neighbors
Increase the dimension Increase the dimension Clustering Clustering Cluster analysis Cluster analysis Check the dimension Check the dimension based on the shape based on the shape
- f the clusters
- f the clusters
≤ − −
2 , ,
) ( ) ( ) ( ) ( j k j y k y
m l m l
ψ ψ
R
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Results I.
) 2 ( ) 1 ( ) 3 ( 125 . ) 2 ( 75 . ) 1 ( 5 . 1 ) ( − + − + − + − − − = k u k u k y k y k y k y
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1 2 3 4 1 2 3 4 1 2 3 4 5 Bemeneti rang Kimeneti rang E IG 1 2 3 4 1 2 3 4 20 40 60 80 100 Bemeneti rang Kimeneti rang FNN (% )
Results II.
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SLIDE 10
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Conclusions
The efficiency of the original FNN algorithm has been increased The idea is based on the geometrical view of the clusters The threshold value is calculated based
- n the shape of the clusters