Soft Sensing - Advanced Control and Supervision of Mineral Processing Plants - page 183

y

ε

ζ 1

ϕ m

ζ m

ϕ 1

V m

y

Figure 4.11 Projection of y into space V m spanned by base B m or the corresponding orthonormal
base B mon

2 im-
plies minimizing the mean square error between y ( e.g. , the primary variable to be
estimated by a soft sensor) and y ( e.g. , the soft sensor output).

ε 2

In particular in a random variable space ε = E ( ) , so minimizing ε

A

y

ε

ϕ θ

ε

1 1

ϕ

ϕ

θ

2

2

y

y

a

ϕ

C

V 2

B

Figure 4.12 Norm ε is minimum if εis orthogonal to the space V 2 spanned by bases ϕ 1 and ϕ 2

The problem at hand is to find the best approximation y of y .Since y belongs to
V m it may be expressed as