Parameter Estimation Methods in Physiological Modeling: An ...
Parameter Estimation Methods in Physiological Modeling: An ...
Parameter Estimation Methods in Physiological Modeling: An ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Sensitivity Identifiability (cont’d)<br />
<br />
Sensitivity Identifiability (cont’d)<br />
Now, let !" = " # " 0 denote a small perturbation from ! 0<br />
. This gives<br />
rise to a small perturbation <strong>in</strong> the output<br />
!y = y(t,") # y(t," 0 ). Then,<br />
by the cha<strong>in</strong> rule for differentiation, we obta<strong>in</strong> the follow<strong>in</strong>g<br />
(approximate)) relationship<br />
!y = S!"<br />
A structure is then said to be sensitivity identifiable if the above<br />
equation can be solved uniquely for<br />
!" . This is the case if and only<br />
the<br />
rank(S) = p, or equivalently, if and only if det(S T S) ! 0 .<br />
GRAZ 2007<br />
It is clear that (local) output dist<strong>in</strong>guishability and sensitivity<br />
identifiability are equivalent concepts.<br />
#<br />
Comput<strong>in</strong>g the sensitivity function matrix S(t,!) =<br />
"y i(t,!) &<br />
% ?<br />
$ "!<br />
(<br />
j '
Change language