Probabilistic Performance Analysis of Fault Diagnosis Schemes

v
w
u
G θ
y
F
r
δ
V
d
Figure 2.3. General parametric fault diagnosis problem. Here, faults affect the system G via the
parameter θ, rather than an exogenous fault signal f , as in Figure 2.2.
2.5 Designing for Reliability
2.5.1 Physical Redundancy
In physically redundant configurations, multiple components performing the same function
are used in parallel. A physically redundant system of four sensors is shown in Figure 2.4.
Note that each identical sensor S is affected by different noises v i , disturbances d i , and
faults f i , making each of the outputs y i different. The outputs are aggregated into a single
measurement ȳ using some sort of averaging or voting scheme. To detect a component
failure, each output y i is subtracted from the aggregate output ȳ to form a residual r i .
Advantages of physical redundancy
Generally speaking, physically redundant systems can survive multiple component failures
and still perform their prescribed function. For example, a quadruplex system of four
components, such as the sensor system in Figure 2.4, can survive two component failures.
After one failure, the failed component is taken off-line and the remaining three components
function in a triplex configuration. Note that the voting scheme must adapt to this new
configuration. If a second failure occurs, the failed component is taken off-line, and the
system functions in a duplex configuration. In the event of a third failure, the system is
unable to determine which component is healthy and which is failed, rendering the whole
system in a failed state.
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