Biomedical Engineering Reference
In-Depth Information
2.5.1 Morris Screening
As discussed by Sin et al. [
11
], an alternative to the linear regression method,
especially when low R
2
values are observed, is Morris screening. Similarly to the
linear regression method, a sampling-based approach is used. The method is based
on Morris sampling, which is an efficient sampling strategy for performing ran-
domized calculation of one-factor-at-a-time (OAT) sensitivity analysis. The
parameters are assigned uniform distributions with lower and upper bounds
defined by the confidence intervals for estimated parameters and by 30 % vari-
ability for the remaining ones (as done previously for the Latin hypercube sam-
pling). The number of repetitions (r) was set to 90, corresponding to a sampling
matrix with 1,080 [90 9 (11 ? 1)] different parameter combinations. The model
was simulated for all the parameter combinations, and the results are summarized
in Fig.
10
.
The elementary effects (EE) were estimated as described by Sin et al. [
12
].
These EEs are described as random observations of a certain distribution function
F, and are defined by Eq.
13
, where D is a predetermined perturbation factor of h
j
,
sy
k
(h
1
, h
2
, h
j
,…, h
M
) is the scalar model output evaluated at input parameters
(h
1
, h
2
, h
j
,…, h
M
), whereas sy
k
(h
1
, h
2
, h
j
? D,…, h
M
) is the scalar model output
corresponding to a D change in h
j
.
Fig. 10 Model simulation results using Morris sampling of parameter space: model simulations
for glucose, ethanol, dissolved oxygen, and biomass showing simulations (blue), mean, and the
10th and 90th percentile of the simulations (black) (not to be confused with uncertainty analysis)
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