next up previous
Next: 6 The Liquid Sodium Up: 5.3 Monitoring Previous: Progressive Monitoring

Temporal Behavior

Fault detection from transients becomes invalid after feedback effects have affected behavior significantly. The monitoring process needs to decide when after time of failure, tex2html_wrap_inline1036 , 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 tex2html_wrap_inline1036 (Fig 14(b)). If a discontinuous magnitude change were present, the transient at tex2html_wrap_inline1036 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 tex2html_wrap_inline1036 . A reverse response constitutes a third phenomenon that occurs for discontinuous changes at tex2html_wrap_inline1036 , 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).

   figure350
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 tex2html_wrap_inline960 and tex2html_wrap_inline1160 , respectively, becomes 0 (after having deviated earlier). Therefore, steady state detection is activated and fault refinement based on transients is suspended.



Pieter J. Mosterman
Tue Jul 15 11:26:35 CDT 1997