Environmental Engineering Reference
In-Depth Information
mum of
T
2
da
mi
Γ
i
[
S
1
(
a
,
Γ
)−
V
1
(
a
,
Γ
i
)]
.
(4.149)
0
For example, in Figure 4.27 the estimated grindability corresponds to medium
ore.
1450
1400
1350
1300
Soft ore template
1250
Sample variance template
1200
Medium ore template
1150
Hard ore template
1100
4
6
8
10
12
14
scale a
(
,
)
Figure 4.27
Templates of CWT variance corresponding to feed ore
F
f
for hard ore and coarse
particle size, for medium ore and normal particle size, and for soft ore and fine particle size, under
normal operating conditions. Also shown is sample variance template
S
1
t
Γ
i
corre-
sponding to a given measurement when the ore grindability in the mill is medium, but unknown
(
a
,
Γ
)
for
F
f
(
t
,
Γ
)
Again, since probability functions are not known, expected values and variances
are computed using time averaged estimators (see Sections 4.2.2 and 4.3.2).
In order to proceed with the process of identifying Γ all templates are converted
into points in a Euclidean space of dimension
M
through discretizing the range of
scale
a
into
M
discrete values
{
a
1
,
a
2
,
a
3
,,
a
M
}
for each template; Figure 4.28 gives
a pictorial view of this conversion.
Further processing includes (i) Concatenation [22] of the three templates corre-
sponding to feed ore flow
F
f
(
t
,
Γ
i
)
,topowerdraw
P
d
(
t
,
Γ
i
)
, and to return ore flow
F
r
and of the sample templates; (ii) PCA to reduce dimensions while retain-
ing relevant information; and (iii) projection to Fisher space for further dimension
reduction and facilitating discrimination between the three possible grindability in-
dexes [22]. Concatenation is a juxtaposition of the templates, so it increases the
Euclidean space dimension from
M
(
t
,
Γ
i
)
42, but this dimension is brought
down to 8 using PCA, and may be further reduced to 2 by projection into the Fisher
space [57]. Figure 4.28 has an equivalence in the PCA space and in the Fisher space.
=
14 to 3
M
=
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