82
Chapter 3
A tD =
0.15 h'1
we find the measured volumetric rates to be (all in C-moles or moles; see Example 3.5)
4 m =
Г-0.14(Л
-0.063
0.063
0.079
(4)
The vector or residuals is then
Є = R r4>
ґ\
,0
0
0.286
1
1
-0.286
0.014
Ґ-0Л 40У
-0.063
_
J
2.0
0.063
[l.l
^
0.079;
(5)
We see that there is fairly good consistency in the data, since the residuals are very small. We will,
however, try to obtain even better estimates for the measured rates.
In order to find the variance-covariance matrix, we need to know something about the size of the
measurement errors. We will here assume that these errors are uncorrelated and that the relative error in the
gas measurements is 10%, whereas it is 5% for the glucose and the biomass measurements. The
variance-covariance matrix is therefore:
F =
^(0.05-0.140)
0
0
0
F = 10“
0
(0.10-0.063У
(
0.490
0
0
о
0
0
0
0
0
0
0.397
0
0
0
0.397
0
0
0
0.157
о
о
о
(0.05-0.079)3
(
6
)
Thus the P matrix is found from Eq. (3.46):
f
1.044
- 0.111
P = R FRf =10 4
-0.111
0.065
p-1
= 10
0.117
0.20f|
0.201
1.887J
(7)
The estimate for the vector of measurement errors can now be calculated by using Eq. (3.48):
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