Environmental Engineering Reference
In-Depth Information
4.4.2.4 Grindability Index Soft Sensor Using Feature Extraction
A grindability index soft sensor has been developed for ore contents in the mill
of the SAG mill circuit is shown in Figure 4.25 [22]. No model was developed
to estimate this grindability index. Instead this index was estimated using features
extracted from three of the measured variables in the circuit: (i) mill power draw
P d ; (ii) return ore flow F r ; and (iii) fresh feed ore flow F f (Figure 4.25). The water
feed flow F w is controlled for a fixed proportion of the fresh feed flow using a ratio
controller. The fresh feed ore flow is the manipulated variable for a PID control of
the total hold-up (ore plus water hold-up) in the mill. Therefore, the feed ore flow
F f depends on the type of ore. For example, if the ore becomes harder the control
reduces the feed ore flow - and conversely if the ore becomes softer - in order to
attain and keep the total hold-up close to its set-point. A similar situation happens if
the feed size distribution changes from finer to coarser.
P d
Water feed
flow F w
SAG
mill
Ore and water
discharge flows
Fresh ore
feed flow F f
Return ore flow F r
Screen
Figure 4.25 SAG circuit for which a grindability index soft sensor was developed based on the
variance of wavelet transforms of measured variables
The feature used in this case is the variance of the continuous wavelet transform
(CWT). The CWT is a transformation
1
a
t
b
W y
(
a
,
b
)=
y
(
t
)
Ψ
(
)
dt
(4.147)
a
of a function y
is the wavelet,
a is the wavelet scale and b is the wavelet displacement. The Haar wavelet shown in
Figure (4.26) has been used here [22].
As seen in (4.147) for a any given scale a , function y
(
t
)
that produces a function W y
(
a
,
b
)
. In (4.147) Ψ
(
t
)
(
t
)
is multiplied by all
possible shifts of the wavelet, and the product is integrated.
The CWT of function y
may be compared with its Fourier transform, and par-
ticularly the Fourier sine or cosine transforms. One difference between these trans-
(
t
)
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