Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 155

4.2 Soft Sensor Models
The task of determining soft sensor models is the same as the general modeling
procedure in which model identification plays a central role. Some important issues
affecting the development of soft sensor models are covered in this section, includ-
ing an alternative way, by analyzing features of measured plant variables. Other
important matters are found in the topics by Fortuna et al. [1] and Ljung [44]. Due
to the particular characteristics of mineral processing units circuits and plants some
special issues are included in this section, such as the introduction of process phe-
nomenology in models which are LIP.
Modeling in mineral processing is generally more difficult than in other indus-
tries. Indeed, some processes here are highly nonlinear (semiautogenous grinding,
flotation) and subject to unmeasured disturbances having a heavy influence on the
controlled variables ( e.g. , grindability, concentrate and tailing grades). In addition,
there is a lack of sensors for on-line measurements ( e.g. , grindability, mineralogy).
For example, Figure 4.2 shows the important effects of unmeasured disturbances in
the case of a concentrate grade soft sensor used in the process of adjusting a flotation
bank phenomenological model to plant data [43]. Since a phenomenological model
would be too complex to use as a soft sensor model or to be included in a model-
based control system, simpler local models have to be developed around operating
points. Therefore, it is to be expected that these models need to be up-dated as the
process operating point shifts. As a consequence, the models are valid only during
limited time spans and these soft sensor models must undergo on-line adaptation
and in some cases off-line adaptation. A compromise must be made between sim-
ple soft sensor models possibly requiring frequent but faster adaptation ( e.g. ,ARX
models [1, 44, 45]) and complex models requiring a less frequent but a slower adap-
tation process ( e.g. , neural networks, and NARMAX models [1, 45]). In between
there are models such as NARX models [1, 45] which are LIP so that adaptation
may be relatively fast, even though they may be non-linear with respect to the plant
measurements. A different approach to soft sensor design is based on the extraction
of features from plant measurements, including images captured by video cameras
( e.g. ,offlotation froth).
The modeling process in the case of soft sensors may be defined paralleling the
definition of identification given by Lotfi Zadeh (Figure 4.3): modeling is the deter-
mination of which model M from a given class of models is the best representation
of the modeled primary measurements for a given class of signals and according to
a given criterion (Figure 4.3), on the basis of only measured variables. Examples of
class of models are difference and differential input-output equations, continuous
and discrete time state-state/output equations, neural networks, wavelet models and
fuzzy models. The criterion often used is the mean square error of some error mea-
sure - such as the one step ahead prediction error or the mean square equation error
(between the plant output and the model output given the values of the measure-
ments contained in the right hand side of the model equation). The class of signals
is concerned with the characteristics of the variables involved in the modeling pro-