The main task is to predict the dynamic qualitative deviations in magnitude and derivatives of the observed variables under the fault conditions. This is called a signature.
The forward propagation algorithm
propagates the effect of faulty parameters along instantaneous and
temporal edges in the temporal causal graph to
establish a qualitative value for all measured system variables.
Temporal edges imply integration, and, therefore,
affect the derivative of the variable
on the other side of the edge. Initially, all deviation propagations
are 0-order magnitude values.
When an integrating edge is traversed in the temporal causal graph
(Fig 7), the magnitude change becomes a
-order (derivative) change, shown by
an 
( 
) in
Fig. 11. Similarly, a first order change
propagating
across an integrating edge creates a second-order (derivative) change
( 
( 
) in Fig. 11), and
so on.
Forward propagation with increasing derivatives
is terminated when a signature of sufficient order is generated
as determined by a measurement selection algorithm [17].
Figure 11: Forward propagation to establish a signature.