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Fig. 8 The data of the multi-
sine input
40
30
20
10
0
0
500
1000
1500
2000
t(s)
12
10
8
6
4
0
500
1000
1500
2000
t(s)
MinPts
¼
40
;
e
¼
:
0
18
The number of submodels obtained with these parameters is (s = 6). The
parameter vectors are illustrated in Table
7
.
The validation results and the estimated titration curves are presented respec-
tively in Figs.
9
and
10
which shows that the obtained model gives good results in
terms of dynamic and nonlinear gain of the pH process.
Now, we compare the performance of the two proposed methods using the
quality measures (
19
), (
20
) and (
21
). The obtained results are summarized in
Table
8
and Fig.
11
.
Table 7 Estimated parameter vectors
Parameter vectors
Estimated values DBSCAN
Estimated values Chiu
h
1
T
T
0
:
9906
0
:
0264
0
:
0218
0
:
9855
0
:
0179
0
:
0101
½
½
h
T
T
0
:
9808
0
:
0287
0
:
0190
0
:
9692
0
:
0593
0
:
0423
½
½
2
T
T
h
3
0
:
9763
0
:
0282
0
:
0152
1
:
0102
0
:
0216
0
:
0200
½
½
h
4
T
T
½
1
:
0272
0
:
0343
0
:
0434
½
1
:
0351
0
:
0273
0
:
0550
h
5
T
T
½
0
:
9968
0
:
0390
0
:
0432
½
0
:
9632
0
:
0289
0
:
0440
h
6
T
T
½
0
:
9690
0
:
0404
0
:
0533
½
1
:
0021
0
:
0903
0
:
0910
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