Fault detection from
transients becomes invalid after feedback effects have affected
behavior significantly.
The monitoring process needs to
decide when after time of failure, , to suspend transient
verification.
Signals may exhibit compensatory
or inverse responses [20].
For compensatory responses the slope becomes 0 (Fig. 14(a)).
For inverse responses, the magnitude and slope deviations have
opposing sign assuming there was no discontinuous change at
(Fig 14(b)).
If a discontinuous magnitude change were present,
the transient at
could manifest as a decrease of this magnitude
resulting in a slope with opposite sign. However, this is not an
inverse response since the transient effects are exactly those as exhibited
at
.
A reverse response constitutes a third phenomenon that occurs for
discontinuous changes at
, and signal overshoot causes
magnitude deviation to reverse sign (Fig 14(c)).
Qualitative observations of magnitude and slope detect these
behaviors from an initial magnitude deviation.
When these situations are detected, transient verification (stage t,
Fig. 14) for that particular signal is suspended
and steady state detection is activated (stage s, Fig. 14).
Figure 14: Qualitative signal transients.
An example of compensatory response in the bi-tank system
is shown in Fig. 13.
At time steps 10 and 26 the first derivative of and
,
respectively, becomes 0 (after having deviated earlier). Therefore,
steady state detection is activated and fault refinement based on
transients is suspended.