Taking an optimal temperature and pH, mopt is the maximum
specific growth rate to be obtained for mmax(aw). The same
accounts for the other factors. As a result, the possible estimation
problem, emerging for the identification of the relation between
mmax and one environmental factor, is minimized. Combining the
experimental results for the multiple conditions forces the model
fitting procedure toward the correct mopt value and, consequently,
to the correct cardinal parameter values.
Secondly, it can be observed that reducing the full factorial
design (64 experiments) to a Latin-square design (12 experiments)
yields equally good parameter values and this for both the equidistant selection and the OED. In the Latin-square design, all
conditions are equally addressed, i.e., four times. In addition, by
selecting the 12 conditions according to the Latin square, the total
experimental space of interest is nicely covered (see Fig. 5 and 7).
This observation agrees with the work of Mertens et al. (2012) who investigated the performance of different designs for the identification of complex square-root models. Based on a simulation study,
it was summarized that, next to the typical full factorial design,
accurate parameter estimates can be observed from a Latin-square
design. As already stressed in the Mertens work, the major differ-
ence between these two types of design is the interpolation region,
i.e., the validity region of the model defined by the outer borders of
the experimental space considered. In the case of a full factorial
design, this cube is defined by the extreme conditions of the
experimental design. For a Latin square, the extremes are different and, therefore, also the interpolation region (see Figs. 5 and 7).
In this case, the validity region can be computed as the
minimum convex polyhedron, introduced by Le Marc, Pin, and
Baranyi (2005).
Taking an optimal temperature and pH, mopt is the maximum
specific growth rate to be obtained for mmax(aw). The same
accounts for the other factors. As a result, the possible estimation
problem, emerging for the identification of the relation between
mmax and one environmental factor, is minimized. Combining the
experimental results for the multiple conditions forces the model
fitting procedure toward the correct mopt value and, consequently,
to the correct cardinal parameter values.
Secondly, it can be observed that reducing the full factorial
design (64 experiments) to a Latin-square design (12 experiments)
yields equally good parameter values and this for both the equidistant selection and the OED. In the Latin-square design, all
conditions are equally addressed, i.e., four times. In addition, by
selecting the 12 conditions according to the Latin square, the total
experimental space of interest is nicely covered (see Fig. 5 and 7).
This observation agrees with the work of Mertens et al. (2012) who investigated the performance of different designs for the identification of complex square-root models. Based on a simulation study,
it was summarized that, next to the typical full factorial design,
accurate parameter estimates can be observed from a Latin-square
design. As already stressed in the Mertens work, the major differ-
ence between these two types of design is the interpolation region,
i.e., the validity region of the model defined by the outer borders of
the experimental space considered. In the case of a full factorial
design, this cube is defined by the extreme conditions of the
experimental design. For a Latin square, the extremes are different and, therefore, also the interpolation region (see Figs. 5 and 7).
In this case, the validity region can be computed as the
minimum convex polyhedron, introduced by Le Marc, Pin, and
Baranyi (2005).
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