Environmental Engineering Reference
In-Depth Information
Model 3
G
s
(
t
−
1
)
f
65
(
t
)=
θ
30
f
65
(
t
−
1
)+
θ
31
)
+
θ
32
.
(4.139)
(
−
)+
(
G
s
t
1
Q
1
w
t
Model 4
θ
41
S
−
3
f
65
(
t
)=
θ
40
f
65
(
t
−
1
)+
(
t
−
1
)+
θ
42
.
(4.140)
p
Model 5
θ
51
S
−
3
f
65
(
t
)=
θ
50
f
65
(
t
−
1
)+
(
t
−
1
)+
θ
52
Q
1
w
(
t
−
3
)+
θ
53
.
(4.141)
p
Tabl e 4. 8
Availability of measurements (I) required for each soft sensor and not required (O)
Soft
sensor
S
p
: % solids
in HC feed
from density
measurement
J
BM
:
Ball
mill
G
s
:
Fresh
feed
Q
1
w
:Sumpwa-
ter addition flow
model
power draw
ore flow
1
I
I
O
O
2
I
O
O
O
3
O
O
I
I
4
I
O
O
O
5
I
O
O
I
Upon detecting a failure at time
t
F
of a measurement affecting the input to the
current soft sensor, the soft sensor shell should give an alarm and possibly replace
the current soft sensor by a soft sensor which does not use the failed measurement.
For example, if
Q
1
w
becomes unavailable, models 1, 2 and 4 may be used, since
they do not depend on this measurement.
As examples, Figures 4.18, 4.19 and 4.20 show the performances of soft sensors
with models 2 and 5 for two periods, with their parameters determined on differ-
ent periods. In particular, in the case of Figure 4.18 and 4.20 there are many long
periods when the actual sensor is down. Nevertheless, an indication that the soft
sensor is performing well is that when the real sensor comes back into operation its
measurement tends to be close to the soft sensor output. The other models also have
satisfactory performances.
4.4.2.2 Global Operational Work Index Soft Sensor
A global operational work index was designed for a grinding plant whose layout
is shown in Figure 4.21 [24]. It consists of a rod mill followed by three sections
in parallel, each one formed by a ball mill in inverse circuit with a hydrocyclone
battery. In this case an empirical relation is combined with an ARX model. The
involved variables are:
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