Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 149

Tabl e 4. 2 Examples of soft sensors for density or solids concentration in ore concentrators
Reference Model

class

Main features Applications, tests

NARX Stepwise regression used to select

SS inputs from set of candidate
components. NARX Gray models
through introduction of compos-
ite components having physical
significance, which are selected
instead of direct simple measure-
ments. Robustness is obtained by
on-line selection of a SS model
from a set of models, using an
availability index

Tests in pulp density using data
from an industrial grinding plant.
The SS model is selected on-line
from a set of four candidate mod-
els.

Casali et al. ,
1995 [16]

NARX Solids concentration soft sen-

sor at hydrocyclone overflow.
Gray models through introduc-
tion of composite components
having physical significance. Se-
lection by stepwise regression

Test using data from industrial
grinding circuit.

Casali et al. ,
1998 [17]

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 using a model
developed for column flotation.

Chuk et al. ,
2005 [18]

ARX Effects of choosing frozen, aver-

age, and optimally predicted soft
sensor parameters at the time of
replacing a sensor by the soft sen-
sor.

Tests for pulp density (solids con-
centration) using data from an in-
dustrial grinding circuit show im-
proved performance

Gonzalez et
al. , 1993 [19]

in case of

predicted parameters.

NARX Stepwise regression. Comparison

between gray and black box (lin-
ear) soft sensor models. Compar-
ison between models with origi-
nal measurements and models in-
cluding phenomenological com-
ponents.

Hydrocyclone overflow particle
size sensor and feed pulp density
(solids concentration) soft sensor
tested using data from industrial
grinding circuit.

Gonzalez et
al. , 1995 [10]

Notation: LIP = Linear-in-parameters; NARX = Nonlinear ARX; NN = Neural Network; SS
= Soft Sensor; PCA = Principal Component Analysis.