Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 76

J ε : part of the reconciliation criterion that contains node imbalances
J ζ : part of the reconciliation criterion that contains driving white noise
K F : projection matrix of the faults in the measurements equations
k : node index
L : matrix for expressing state variables for independent state variables
L F : projection matrix of the faults in the conservation equations
L : Lagrangian function

m: number of measured process variables
m i : vector of component i hold-up in the various nodes of the plant network
m 0 : mass hold-ups of total material
M dep and M ind : matrices associated to dependent and independent state variables
M i : network incidence matrix for component i
M : incidence matrix of the plant network for all the stream components
M m and M um : incidence matrices for measured and unmeasured state variables
M 0 : incidence matrix for total mass
M s : sample mass
n : number of components in plant streams (total mass not included)
n X : number of state variables
n n : number of plant network nodes
p : number of streams in the plant network
P i : production rate of the component i
q : number of conservation equations
Q Q : functions or coefficient matrices in the deductible part of the constraint

equations
r : residuals of the redundancy equations (vector in parity space)
R or R

Q ,

,

:coefficient matrix or function in the redundancy equations
s : vector of node separation coefficient of a mineral separation plant
s ki : component i separation coefficient at node k
S

( Y )

: contributions of the measurement errors to the parity vector
T or T

( e )

( ε ) : contributions of the constraint uncertainties to the parity vector

Var : statistical estimate of the variance of a process variable

V X : variance of the reconciled states
V x

(.)

( k ) , V x : autocovariance of any process variable x and variance ( i.e. , V x ( 0 ))

V : variance of the measurement errors e
V ε V ε i : variances of εand ε i

V f :varianceof f
V i :varianceof c i
V in : variance of the innovations
V r :varianceof Y r
V Y : variance of the reconciled measured variables
V δ

,

, ( ) ( )

V ω : variance of white noise δ t or ω t

X : state variable
X m : measured state variables
X mr , X mr : redundant measured state variables and reconciled value
X o , X or , X onr : observable state variables (redundant and non-redundant)