Environmental Engineering Reference
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made to change at will. Therefore, if they have an effect on some of the soft sen-
sor components, and if measured disturbances are not sufficiently variable in a
parameter estimation interval, the model may not adequately reflect their influ-
ence on dynamic conditions. Parameter updating may be performed using a time
window or a recursive parameter estimation method using fixed or variable for-
getting factors [44]. In any case it should be considered that the variance of the
estimated parameters, which affects the soft sensor output, depends on the win-
dow length, or on the value of the forgetting factor in recursive estimation. As in
many estimation problems a compromise must be made between having a small
estimator variance and speed in achieving the parameter estimation. In general,
subjecting the plant to excitation conditions may unduly alter the production ob-
jectives. But since proper excitation is needed for an adequate determination of
model parameters, a compromise should be reached between length and magni-
tude of the excitation and the possibility of losing the information provided by
the soft sensors when the actual sensors become unavailable.
6. Parameter selection module. This module uses past data to predict the parameter.
At the moment of replacement this module decides whether to use frozen param-
eters values, their mean values, or their prediction according to the quality of the
parameter prediction or expected value estimation, verified while the sensor is
operating [19]. See also Section 4.2.4.
7. Sensor fault detection module. This function includes the detection of a fault in
any sensor providing required secondary measurements for the model compo-
nents, as well as in the primary measurement sensor. Fault detection and identi-
fication methods may be found in [1] and [67].
4.4.2 Soft Sensors for Grinding Circuits
4.4.2.1 Particle Size Soft Sensors
A particle size soft sensor has been designed to replace a real sensor which mea-
sures the proportion of particles retained by 65# in the hydrocyclone overflow of an
industrial grinding circuit of a large copper concentrator. The layout of the grinding
circuit is shown in Figure 4.17. A conveyor belt conveys the fresh feed ore to the
sump where it is mixed with the sump water addition and the hydrocyclone reject
flow. The sump discharge flow is pumped to the hydrocyclone feed. The hydrocy-
clone overflow is conveyed to a flotation plant. Measured circuit variables are given
in Table 4.9.
The approach to robustness used here is through selection of the best available
model out of a set of candidate models for the soft sensor.
Collected data.
Three sets of data were used:
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