Page 421 - Design of Simple and Robust Process Plants

408 Chapter 9 Operation Optimization
The4 following variance of the validated measured variables are obtained:
m
2
var (X i )= P N i;j W j;j † X †
0
j
jˆ1
for the estimated unmeasured variables:
m
2
var (Y i )= P N n‡i;j W † X †
0
j;j
j
jˆ1
Taking into account:
var (X¢ j )=1/W jj
now:
m
2
var (X i )= P N = X †
0
j
i;j
jˆ1
M
var (Y i )= P N 2 n‡i;j =var X †
0
j
jˆ1
The contribution of the variance of measurement k in the estimation of the var-
iance of reconciled state variable i is derived from the equation above:

0
var X i †var X †
Contribution k,i = k
M †i; k 2
1
The sensitivity coefficient relating the validated variable to the measured value
and the standard deviation are:

DerVal k,i = dX k DerAcc k,i = dX k
dX i d i
The analysis technique to determine the accuracy of the reconciled data has been
developed by Heyen (1994)and further extended by Heyen et al. (1996).
References
Albers J.C. On line data reconciliation and Belsim. Alee des Noisetiers B4301 Angleur
error detection. In: Advanced Process Liege Belgium E-mail:
Control and Information Systems for the hotline@belsim.arc.be User Group
Process Industries (Kane, L.A., Ed.), Gulf Meeting, Antwerp, April 1994.
Publishing Company, 1999, pp. 136±139. Britt, H.I. and Luecke, R.H. The estimation of
ISBN 0-88415-239-1. parameters in nonlinear implicit models.
Albers J.C. Data reconciliation with Technometrics 1973, 15, 233±247.
unmeasured variables In: Advanced Process Factora F.C., Gochenour, G.B., Houk, B.G.
Control and Information Systems for the and Kelly, D.N. Closed loop real time
Process Industries (Kane, L.A., Ed.), Gulf optimization and control of a world scale
Publishing Company, 1999, pp. 140±142. olefins plant. Lyondell PetroChem Co. &
ISBN 0-88415-239-1. DMC Corp., AIChE meeting, Spring 1992.