Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 75

6. As the success of data reconciliation methods strongly depends on the database
structure, it can be used to design measurement strategies that promote estimate
accuracy and reliability.

Nomenclature
The notation that is specific to illustrative examples in the text is not defined below.
Roman letters
A

B : matrices of coefficients in a state space stochastic model
b : measurement bias
B

A , , B ,

: matrix function of the separation coefficients for steady-state modeling of a
separation plant
c : composition factor
c i and c i : concentration of component i and reconciled value
C : measurement coefficient matrix in the linear case
C f : measurement coefficient matrix for the total mass flowrates
C i : measurement coefficient matrix for the component i concentrations
C i : diagonal matrix constructed with the vector c i
d : sieve opening retaining 25% of the particles
d lib : particle liberation size
D i

(.)

F i : matrices of coefficients associated to component i
e I : integration error
e r : measurement error of the redundant measured variables
e f : measurement error of the total mass flowrates
E

, E i ,

(.) : mathematical expectation

f : constraints of mass or energy conservation

f : vector of all the component flowrates (or shape factor in Section 2.4)
f i : vector of component i flowrates in the plant network
f i

( X )

: i th reconciliation constraint
f 0 :totalmassflowrate vector
f 0 : f 0 mean value
f : f mean value
F 0 : diagonal matrix of the vector f 0
F X

(.)

F Y : Faults in the conservation and measurements equations
F,F

,

,F

b : Union of the faults sets F X and F Y and two complementary subsets of a

it.
g : size distribution factor
g ( X ) : expression defining the measured variables

z −

1

G : discrete transfer function

h : time window width
h

( )

: function of the independent variables
h i : component i mass fraction in node hold-ups
i : index of the steam components i
in : innovations of the reconciliation procedure
I : identity matrix
J

(.)

: reconciliation criterion
J m : part of the reconciliation criterion that contains measurements

( X )