Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 148

Tabl e 4. 1 Examples of soft sensors for particle size in grinding circuits

Reference Model

class

Main features Primary variable, applications,

tests

ARX Static particle size estimator with

dynamic compensator.

+65 # for grinding circuit consist-
ing of a rod mill and a ball mill.

Gonzalez et
al. , 1985 [9]

NARX Stepwise regression. Comparison

between gray and black box
NARX soft sensor models. Ef-
fects due to improper sampling
period.

Tests using data from industrial
grinding circuit for estimating
or predicting % +65# in circuit
product. Sampling period effects
tested in simulated simple plant.

Gonzalez et
al. , 1995 [10]

NARX Stepwise regression. Robustness

to secondary measurements fail-
ures using a set of candidate soft
sensor models. Gray models us-
ing composite candidate regres-
sors determined by phenomeno-
logical model.

Tests using data from industrial
grinding circuit for estimating
or predicting % +65# in cir-
cuit product. Stepwise regression
selects mainly phenomenological
regressors instead of direct sec-
ondary measurements.

Casali et al. ,
1998 [11]

NN NN soft sensor for particle size in

product of grinding circuit con-
sidering adaptation to changing
conditions. Use of PCA to sim-
plify the SS model in order to im-
prove on-line adaptation perfor-
mance.

Tests using simulated industrial
grinding circuit. SS estimates
passing 53 μm particle size.

Du et al. ,
1997 [12]

NARX Adaptation of soft sensor model

parameters to changing condi-
tions considering parameter con-
straints using the error projection
(EP) algorithm. Regressors in-
volving inputs in LIP NARMAX
model are convolutions.

Tests using data from industrial
grinding circuit for estimating
or predicting % +65# in circuit
product. Comparison of EP and
RLS algorithms.

Sbarbaro et
al. , 2008 [13]

NN Feedforward and autoassociative

NN are used as soft sensors
for particle size. After selection
of model input variables (sec-
ondary measurements) NN pa-
rameters are determined using the
Levenberg-Marquardt algorithm

Tests using data from industrial
grinding circuit for estimating or
predicting % +65#. Comparison
of NN models used concerning
input noise and number of param-
eters.

Sbarbaro et
al. , 2001 [14]

SVM Particle size soft sensor model de-

signed by combining SVM, iden-
tification, and empirical meth-
ods weighted according to perfor-
mance of each.

Tests using particle size data form
industrial grinding circuit. One
hour sampling time over 23 days.

Sun et al. ,
2008 [15]

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