Calculation of variance
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Calculation of variance


DisciplinaProcessamento de Minerais I198 materiais2.050 seguidores
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mineral processing flowsheet. This is presented in an other publication
(Hodouin et al., 1998).
7. Nomenclature
ai .t/ flowrate of species i at time t
ain average of n equally spaced values of ai .t/ in a window of width N T
A, B, C coefficients of the state\u2013space model of the species flowrates (matrices)
eF material flowrate integration error
eai ith species content integration error
exi ith species flowrate integration error
F.t/ or Fj.t/ material flowrate at time t in the jth stream
Fn or Fjn average of n equally spaced values of F.t/ or Fj.t/ in a window of width
N T
g; g0 model coefficients
G first-order discrete transfer function
h Gy\u2019s heterogeneity
k number of discretization periods separating two sampling instants
k0 number of discretization periods corresponding to the first sample in the
window [0; N T ]
l number of discretization periods for the estimation of an autocovariance
m number of species in the processed material
n number of samples in a window [0; N T ]
N number of discretization periods in a window [0; N T ]
p number of streams in the flowsheet
s marginal separation coefficient of a mineral separation device
t time index (integer corresponding to the number of discretization periods)
T discretization period
A. Mirabedini, D. Hodouin / Int. J. Miner. Process. 55 (1998) 1\u201320 19
V .n; k/ variance\u2013covariance of the integration error of y.t/ for n samples sepa-
rated by k discretization periods
Vyy.0/ variance\u2013covariance of y.t/
Vyy.l/ autocovariance of y.t/ at lag l
Vzz.l/ autocovariance of z.t/ at lag l
V\ufffd variance\u2013covariance of \ufffd
xi .t/ ith species flowrate
xi j .t/ ith species flowrate in stream j
xin average value of n samples of xi.t/ in the window [0; N T ]
y.t/ vector of species flowrates xi j .t/
yn average value of n samples of y.t/ in [0; N T ]
z\ufffd1 backshift operator
z.t/ state variable of the flowrate dynamic model
\ufffd, \ufffd, 
 model coefficients
\ufffd mean value of y.t/
\ufffdi j mean value of xi j .t/
\ufffd 2i j variance of xi j.t/
\ufffd.t/ white noise
Acknowledgements
This study is part of a generic project on the application of automatic control to
the mineral processing and extractive metallurgy industries. It is supported by the
Natural Resources Departments of the Quebec and Canada Governments as well as by a
consortium of fourteen Canadian mining companies.
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