Environmental Engineering Reference
In-Depth Information
X
o
: reconciled value of
X
o
X
no
: non-observable state variables
X
um
: unmeasured state variables
x
i
: state variable associated to component
i
x
: any generic process variable (scalar or vector)
x
s
: sample mineral content
x
∗
: true value of the mineral content of a sampled batch
X
: reconciled state variable
X
dep
: dependent state variables
X
ind
: independent state variables
X
ind
: reconciled independent state variables
X
dep
: reconciled dependent state variables
Y
: measurement values
Y
f
: measurement values of
f
Y
i
: measurement values of component
i
mass fractions
Y
nr
: measured values of the non-redundant measured variables
Y
r
: measured values of the redundant measured variables
z
: state space variables of a stochastic system
z
−
1
: backshift operator
Z
: measured variables
Z
nr
: non-redundant measured variables
Z
r
: redundant measured variables
Greek letters
ε: overall conservation constraint uncertainties
ε
0
: uncertainty of the total mass conservation equation
ε
i
: uncertainties in the conservation constraints of component
i
in the plant network
γ
i
: auxiliary matrix in the node imbalance solution
δ
: uncertainties in the process dynamic model
λ: Lagrange's multipliers
ξ
i
(
t
)
, ξ
(
(
t
)
, ξ
(
t
)
t
)
: white noise
: white noise driving uncertainties in the process dynamic model
μ
x
: mean value of
x
σ
e
: standard deviation of the measurement error
e
σ
F
: standard deviation of the fundamental sampling error
σ
X
: standard deviation of the reconciled states
Γ: auxiliary matrix in the linear reconciliation case
ρ
v
: degree of variance reduction
ρ
ξ
d
(
t
)
: autocorrelation matrix
ρ
gan
: gangue density
ρ
min
: mineral density
ρ
r
: degree of redundancy
Ψ and Φ:coefficient matrices in the linear case reconciliation information system
ψ: matrix that extracts the node output streams from the vector
f
i
ϕ(.): function defining the node hold-ups
(
k
)
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