Probabilistic Performance Analysis of Fault Diagnosis Schemes

1
P tn,k
0.8
P fp,k
P fn,k
(a)
Probability
0.6
0.4
P tp,k
0.2
0
1
0 5 10 15 20 25 30
P d,k
0.8
P f,k
Q 0,k
(b)
Probability
0.6
0.4
0.2
0
0 10 20 30 40 50 60
Time (min)
Figure 6.8. Performance metrics for the vtol aircraft example with observer gain L 1 . Plot (a) shows
the joint probability performance metrics, and plot (b) shows the conditional probability performance
metrics. Note that the sequences {P fn,k } and {P tp,k } are barely distinguishable from zero.
Table 6.2. Steady-state values of the performance metrics for the vtol aircraft example. For each
observer gain L i , the steady-state value is taken to be the value achieved at the final time step N .
Performance Metrics
Gain P tn,N P fp,N P fn,N P tp,N P f,N P d,N
L 1 0.9735 0.02439 1.082 × 10 −5 1.998 × 10 −3 0.02444 0.9946
L 2 0.9735 0.02439 4.496 × 10 −5 1.965 × 10 −3 0.02444 0.9776
L 3 0.9735 0.02439 1.082 × 10 −5 1.998 × 10 −3 0.02444 0.9946
113