Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 146

linear models ( e.g. , ARX, ARMAX) and at the same time share the linear regression
possibilities of linear models.
Soft sensor design must be approached not only considering the design of the soft
sensor model. In addition a soft sensor shell providing robustness for the primary
measurement estimation is needed, mainly in case secondary measurements may
themselves become degraded and even unavailable and also because of changes in
operating points not dealt with by the soft sensor model. The main functions of the
soft sensor shell system are signal conditioning and monitoring, determining that the
primary sensor has failed in some sense (including loss of calibration), on-line deter-
mination of which soft sensor model of a possible set of models is best for replacing
the unavailable actual sensor, adaptation of the soft sensor models to changing plant
conditions, providing adequate excitation of plant inputs for on-line estimation of
the model parameters, etc. If conditions previous to sensor replacement by the cor-
responding soft sensor are favorable, it may become convenient to choose the model
parameters using their optimal prediction rather than fixed values at the replacement
instant. The soft sensor shell and its main functions are treated in Section 4.4.
Section 4.3 contains a geometric approach to the subject of soft sensor modeling
in the case of linear models or nonlinear models that are LIP. A global approach to
modeling LIP models is taken with respect to the kinds of primary and secondary
variables, whether they are represented by deterministic time sequences, discrete
time stochastic processes ( i.e. , random sequences), or continuous time functions and
stochastic processes. The issue of using time averages instead of expected values is
considered, together with conditions that allow the averages to be valid represen-
tations of expected values. This is important because the use of expected values is
generally the appropriate way to approach the problem of model structure deter-
mination and parameter estimation. However, probability distributions are mostly
not available for determining expected values, so they must be estimated by their
corresponding time averages.
An additional problem to be considered when a sensor in a control loop is re-
placed by a soft sensor is the effect that this change may have on the performance of
the control, since now the control loop contains the additional system constituted by
the soft sensor model. This fact may cause deterioration of control and even insta-
bility as the plant operating point changes unless the model is updated fast enough
(Section 4.2).
The use of soft sensors has become wide-spread in different industries, particu-
larly in the mineral processing industry. A sample of the soft sensors currently used
in this industry and of the different classes of models that are being used is given
in Tables 4.1 to 4.4, which show that soft sensors have been developed for particle
size in grinding circuits, density or solids concentration, grindability, work index,
operational work index, lithology, grades in flotation cells, weight and flow. This
sample is not intended to be exhaustive, but its purpose is to cover the scope and
most of the approaches concerning soft sensor design and operation with regard to
the mineral processing industry. For each soft sensor, this set of tables contains the
reference citation, the class of model used, its main features, and its application in
the industry or to tests performed using data obtained from industrial plants or from