Biomedical Engineering Reference
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Fig. 6 Representation of uncertainty in the model predictions for glucose, ethanol, dissolved
oxygen, and biomass: Monte Carlo simulations (blue), mean, and the 10th and 90th percentile of
the predictions (black)
(in absolute value) will lead to an elliptical or linear cloud of sampling points, as,
for example, for Y X Oxid and Y XG
Red [corr(Y X Oxid , Y XG
Red ) =-0.98 in Table 8 ], as well as
r E,max and K E , and r O,max and K O .
The number of samples and the assumed range of variability of each parameter
(i.e., the parameter space) is defined by the expert performing the analysis. The
higher the number of samples, the more effectively the parameter space will be
covered, at the expense of increased computational time. The range of the
parameter space should rely on previous knowledge of the process: (1) the initial
guess of the parameter numerical values can be obtained from the literature or
estimated in a first rough estimation where all parameters are included; (2) the
variability (range) for each parameter can be determined by the confidence
intervals, in case a parameter estimation has been done, or be defined based on
expert knowledge as discussed by Sin et al. [ 12 ].
The estimations for the four model variables (outputs) and the corresponding
mean and a prediction band defined by 10 and 90 % percentiles are presented in
Fig. 6 . The narrow prediction bands (including 80 % of the model predictions) for
glucose reflect the robustness of the predictions for this model variable, while the
wide bands observed, for example, for oxygen show the need for a more accurate
estimate of the parameters in order to obtain a good model prediction.
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