Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 152

Tabl e 4. 4 Examples of soft sensors for grades and density in flotation

Reference Model

class

Main features Applications, tests

Dynamic
and static
empirical
models

SS based on transfer function
model empirical relations for
froth density estimation in col-
umn flotation used in conjunction
with expert fuzzy system to pre-
vent froth collapse.

Tests by simulation.

Chuk et al. ,
2005 [18]

ARX Stepwise regression. Comparison

of concentrate grade soft sensors
with and without clustering.

Tests of rougher flotation grade
using data from an industrial
grinding plant. Clustered SS
gives remarkably better RMS and
correlation.

Espinoza et
al. , 1995 [26]

NARX Concentrate grade SS. Stepwise

regression. Gray models. Com-
parison between soft-sensor mod-
els (large prediction span) and
control

Tests using data from an indus-
trial rougher flotation plant and
from a model.

Gonzalez et
al. , 1994 [30]

models (low prediction

span and forcible inclusion of

some manipulated variables).

Various Local soft sensor models us-

ing various models stemming
from a general model struc-
ture: ARMAX, NARX NAR-
MAX, cluster, neural networks,
fuzzy Takagi-Sugeno, and com-
binations of them. Comparisons.
Data

Test using concentrate grade data
from industrial rougher flotation
plant .

Gonzalez et
al. , 2003 [31]

validation for soft-sensor

design.

Extraction
of fea-
tures of
measured
variables
(images)

SS giving froth characteristics on
the basis of froth image analysis,
including characteristics dynam-
ics.

Installed in flotation plant and

used in expert control loops.

Hyotyniemi,
2000 [32]

Notation: LIP = Linear-in-parameters; NARMAX = Nonlinear ARMAX; NN = Neural Net-
work; SVM = Support Vector Machine SS = Soft Sensor; PCA = Principal Component Anal-
ysis; RMS = root mean square;