Next, a forward propagation algorithm predicts dynamic qualitative deviations in magnitude and derivatives of the observations 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 signature for all observations.
Temporal edges imply integrating
effects, and, therefore, affect the derivative of the variable
on the other side of the edge. Initially, all deviation propagations
are 
order magnitude values.
When an integrating edge is traversed, the magnitude change becomes a
-order (derivative) change, shown by
an 
( 
) in the temporal
causal graph (Fig. 4). Similarly, a first order change
propagating
across an integrating edge creates a second-order (derivative) change
( 
( 
) in Fig. 4), and
so on.
Figure 4: Forward propagation yields signatures.
Forward propagation with increasing derivatives is terminated when a signature of sufficient order is generated as determined by the measurement selection algorithm [6, 9, 7]. A complete signature contains derivatives specified to its sufficient order. When the complete signature of an observed variable has a deviant value, monitoring should report a non normal value for this variable.