Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 171

all possible subsets of candidate components are systematically determined in order
to choose the best one. It also has options for the forward inclusion or forward
regression method [48] and various criteria for assessing the best model.
Good results have been obtained by Casali et al. [11, 16, 17] and by Gonzalez
et al. [10, 31] using stepwise regression in the design of soft sensors for grinding
circuits and flotation concentrate grades.

p

y

u

PLANT

v

ξ 1 ξ 2 ξ 4 ξ 5 y

ξ 3

Phenomenological
Knowledge

Set of
Candidate
Components

ϕ 1 ϕ 2 ϕ k ϕ ν

Selection of

Model Components

ϕ κ

ϕ j ϕ σ ϕ p

y

Model

Figure 4.6 Example of a structure determination for a black box model, where the candidate com-
ponents are measured variables or functions of them, derived from phenomenological knowledge
about the plant. The manipulated variables are in vector u . Vector v contains the measured distur-
bances and vector p the unmeasured disturbances

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

200 400 600 800 1000 1200 1400

Figure 4.7 Evolution of the relative membership functions ψ 1 and ψ 2 used to combine the outputs
of models 1 and 2 corresponding to clusters C 1 and C 2 in the design of a concentrate grade soft
sensor for a rougher flotation bank (from [31])