Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 174

ral network models tend to be valid in larger operating regions, but updating takes
longer [12].
4.2.4.7 Support Vector Machines (SVM)
Support vector machines have recently started being used [60] for designing soft
sensors for the mineral processing industry. Sun et al. [15] have used SVM in the
design of a particle size soft sensor at the hydrocyclones overflow in an industrial
grinding circuit.
4.2.5 On-line Parameter Estimation
Once a model structure has been determined, the model parameters (weights) are
estimated for an operating region. For this purposes gradient techniques are used
to minimize a function of an error by measuring the discrepancy between the plant
measurement and the estimated measurement obtained using the model ( e.g. ,the
mean square prediction error or the output error). For certain cases such as ARX
and NARX models explicit solutions are available and no search for the optimum is
necessary (Section 4.2.2).
As already pointed out, model parameters may have to be updated as the oper-
ating point moves within a region - e.g. ,defined by clusters - even if the structure
remains valid. Parameter estimation may be performed on-line or off-line, depend-
ing on whether there is an installed operating sensor for the primary measurement
or not. If this sensor is not installed, sampling and laboratory measurements would
be required. In the off-line case the model should be valid in a large operation region
so that the model parameters do not need to be updated frequently, because of the
operational and cost matters involved.
A model based on the slower than appropriate sampling rate will not give sat-
isfactory results, since it is derived using samples that do not represent the actual
evolution of the variable involved. Instead, a model must be built using a sampling
rate that is fast enough for the sampling theorem to be satisfied [61]. If there are
other correlated secondary measurements that are sampled at an appropriately fast
rate there is a solution. A model is built based on the fast sampling rate, notwith-
standing which its parameters (weights) may be found using the infrequent samples
provided by the measurement of the modeled primary variable as well as the fast
rate samples of the correlated (secondary) measurements. For example, an instru-
mentation system for measuring grades in a flotation plant is used in a time sharing
mode to assay 14 samples piped into an X-ray analyzer. If the analyzer takes 30 s to
measure each mineral sample, the sampling rate for any of the 14 measured grades
is 7 min. In a similar case there is a laboratory analysis performed infrequently on
the modeled variable but due to the dynamics of the process a faster rate is required
for good manual or automatic control [33, 62].