Biomedical Engineering Reference
In-Depth Information
4.1 Application areas in Bioprocessing
Luttmann et al. [
33
] provide a status report on the use of software sensors in the
bioprocess area, highlighting industrial implications in particular. All aspects of
bioprocessing, from raw material and seed quality assessment, through bioreactor
monitoring for a range of microbial and cell culture processes, to downstream
process monitoring, are discussed in the report with relevant examples drawn from
literature sources.
A range of modelling methods are used in software sensors, although from the
perspective of this chapter, those of most interest are the MVDA regression
methods. These can be broadly divided into linear and non-linear methods, and the
most frequently used methods are described in
Sects. 4.2
and
4.3
with reported
bioprocess applications of each technique.
4.2 Linear Regression Methods
Although a range of simple linear regression models, including multiple linear
regression (MLR) and principal component regression (PCR) [
14
], have been used
to correlate cause (X) and effect (Y) variables for a range of processes, the partial
least squares (PLS) method and its variations are arguably the most frequently
used MVDA regression tools in this application area. The PLS algorithm operates
by projecting the cause and effect data onto a number of latent variables and then
modelling the relationships between these new variables (the so-called inner
models) by single-input single-output linear regression as described by Eqs. (
3
)
and (
4
):
X
¼
X
np\nx
t
k
p
k
þ
E and Y
¼
X
np\nx
u
k
q
k
þ
F
ð
3
Þ
k
¼
1
k
¼
1
where E and F are residual matrices, np is the number of inner components that are
used in the model and nx is the number of causal variables,
u
k
¼
b
k
t
k
þ
e
k
ð
4
Þ
where b
k
is a regression coefficient, and e
k
refers to the prediction error.
Whilst the PLS algorithm is developed as a method of dealing with large-
dimensional data sets, the multianalyte measurement methods, such as NIR or 2D
fluorescence spectroscopy (Chap. 1), being introduced more frequently into bio-
process monitoring, often lead to data sets with a very large number of variables,
particularly when combined with a number of traditional process measurements or
with data collected from other unit operations up- or downstream of the investi-
gated unit. Building separate models representing individual unit operations and
even individual measurement techniques is an approach that can be used to address
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