Probabilistic Performance Analysis of Fault Diagnosis Schemes

Chapter 1
Introduction
In safety-critical applications, a system must not only be highly reliable, but that reliability
must be certifiable in some way. For example, the Federal Aviation Administration (faa)
requires designers of civil aircraft to demonstrate that their products will have no more
than 10 −9 catastrophic failures per flight-hour [18]. Such demonstrations are based on two
factors: the reliability of the system hardware in a given operating environment and the
ability of the system to detect when that hardware has failed. In the aviation industry, both
of these issues are addressed by the use of parallel redundant components [18,103,104]. This
type of redundancy, known as physical redundancy, ensures the availability of the system,
even in the presence of component failures. In a physically redundant configuration, a failed
component is detected by directly comparing the behavior of each redundant component.
Hence, these schemes tend to detect faults accurately, and their performance is relatively
simple to certify using fault trees [41, 77].
However, in some applications, such as unmanned aerial vehicles (uavs), the designer
cannot afford the extra size, weight, and power needed to support multiple redundant components.
In such situations, the analytical redundancies between dissimilar components
can be exploited to detect faults. More specifically, mathematical models of the system are
used to establish analytical relationships that hold only when the constituent components
of the system are functioning properly. Then, when a component fails, one or more of these
relationships is violated and the failure can be detected and diagnosed. This approach,
known as model-based fault diagnosis [24, 48], certainly reduces the number of individual
components needed; however, there are two main drawbacks to consider. First, merely identifying
a fault cannot prevent system-wide failure if the failed component is indispensable
(i.e. no other components can perform the same critical function). Second, the performance
of fault detection schemes based on analytical redundancy can be difficult to quantify if the
analytical relationships are dynamic or nonlinear. While the first difficulty is unavoidable,
this dissertation addresses the second difficulty.
Although there is a vast body of literature on model-based fault diagnosis (see [9, 24, 48]
and references therein), little attention is given to the rigorous performance analysis of
model-based fault diagnosis schemes. In this dissertation, we present a set of probabilis-
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