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Table 9 Estimated parameter vectors with the proposed clustering techniques
Parameter
vectors
Estimated parameters with Chiu
Estimated parameters with DBSCAN
2
4
3
5
2
4
3
5
h 1
1
:
4256
1
:
4404
0
4508
4 : 9853 10 4
0 : 0010
:
0
4692
0 : 0003
0 : 0014
:
2
4
3
5
2
4
3
5
h 2
1
:
1604
1
:
1144
0
:
2111
0
:
1772
0
0015
0 : 0014
:
0
0003
0 : 0032
:
2
4
3
5
2
4
3
5
h 3
1 : 0847
0
1 : 0591
0
1490
:
:
1304
10 4
3
:
9782
0
:
0006
0
:
0040
0
:
0034
cation procedures in order to represent the reactor
by a PWARX model. The number of neighboring is chosen n q ¼
We apply the proposed identi
70 with the two
proposed techniques. Our purpose is to estimate the number of sub-models s, the
parameter vectors
h i ð
k
Þ;
i
¼
1
; ...;
s and the hyperplanes de
ning the partitions
s
i
H fg
1 .
The obtained results are as follows:
¼
The number of sub-models is s =3.
￿
The parameter vectors
h i ð
k
Þ
, i
¼
1
;
2 and 3 are illustrated in Table 9 .
￿
The attribution of every parameter vector to the submodel that has generated it is
ensured by the SVM algorithm. The obtained outputs are then computed and they
are represented in Fig. 15 .
(a)
(b)
110
110
100
100
90
90
80
80
estimated y
real y
70
70
60
60
50
50
40
40
30
30
estimated y
real y
20
20
10
10
0
50
100
150
200
250
0
50
100
150
200
250
k
k
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