Environmental Engineering Reference
In-Depth Information
Plant
z(t, ξ )
Expected Value
(mean in ξ)
Time Average
A T ( ξ )
E
{ z
msc
Ergodicity
Figure 4.16 The ergodic property causes convergence in the mean square of estimator A T
(
ξ
)
to
E
{
z
}
( i.e. , the variance of their difference tends to 0 as T tends to infinity)
For the case treated here it may be shown that the random estimation vector is
unbiased and that its variance tends to zero as the length T of the time window tends
to infinity [44].
4.4 Soft Sensors in Industrial Concentrators
This first part of this section deals with actions that must be taken in order to en-
sure the availability of soft sensors. The second part gives some examples of soft
sensor design and testing for industrial plants using actual plant data. Two cases are
considered in some detail: (i) model based - a soft sensor for particle size and an
operational work index soft sensor; and (ii) feature extraction based - a soft sensor
for grindability estimation. More cases of soft sensors in mineral processing plants
may be found in the references given in Tables 4.1 to 4.4 in the Introduction.
4.4.1
Soft Sensor Management Systems
From an industrial point of view a soft sensor must be reliable and robust, otherwise
its main purpose, serving as an alternative for obtaining a measurement when a real
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