Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 194

Tabl e 4. 7 Measured grinding circuit variables

Symbol Description Units

/

G s Fresh feed ore flow t h

J BM Ball mill power draw kW

m 3

Q 1 w Sump water addition flow / h

cm 3

S p Solids proportion in hydrocyclone feed pulp S p

Solids proportion in the hydrocyclone feed pulp,
computed using the measurement of the pulp den-
sity

g /

f 65 Mass proportion of particles retained at 210 μm

mesh (+65#) in the hydrocyclone overflow

%65#

• Data Set 1. Data collected during four days of month 1 was used to determine
the structure of the models. From this data set the period during which the plant
appeared to be sufficiently excited was used.
• Data Set 2. Data collected during four days of month 2.
• Data Set 3. Data collected during days three additional days of month 2. It was
used for tests including parameter updating of soft sensor models designed with
Data Set 1.
Model determination.
The model structures were determined by means of the stepwise regression
method, which sequentially selects model components (regressors, components,
bases) from a set of candidate components [11, 48]. See also Section 4.2.4. Follow-
ing the approach by Gonzalez et al. [10], the set of candidate components not only
includes plant measurements (ore and water flows, densities, particle size, power)
but also functions of these measurements determined using a phenomenological
model of the grinding circuit according to the approach given by Casali et al. [11]
and Gonzalez et al. [10].
From a phenomenological model more than 100 possible composite components
(bases) were found for building LIP models. These composite regressors are non-
linear functions of the measured variables and, as pointed out in Section 4.2, make
it possible to extend the validity of the models, for a given parameter set, to an op-
erating region that may be much broader than if only direct plant measurements are
used. In this way, a nonlinear model but which is linear in the parameters is used,
i.e. , a NARX model, and linear regression may be employed.
In order to ensure the availability of the estimated +65#, soft sensor models were
designed for the cases in which some measurements affecting the soft sensor com-
ponents became unavailable. Therefore, when determining models for which a mea-
surement was purposely omitted, components which are function of these omitted
measurements are also omitted.
The composite regressors chosen from the candidate set by stepwise regression

are