Probabilistic Performance Analysis of Fault Diagnosis Schemes

Abstract
Probabilistic Performance Analysis of Fault Diagnosis Schemes
by
Timothy Josh Wheeler
Doctor of Philosophy in Engineering–Mechanical Engineering
University of California, Berkeley
Professor Andrew K. Packard, Co-chair
Professor Peter J. Seiler, Co-chair
The dissertation explores the problem of rigorously quantifying the performance of a fault
diagnosis scheme in terms of probabilistic performance metrics. Typically, when the performance
of a fault diagnosis scheme is of utmost importance, physical redundancy is used
to create a highly reliable system that is easy to analyze. However, in this dissertation, we
provide a general framework that applies to more complex analytically redundant or modelbased
fault diagnosis schemes. For each fault diagnosis problem in this framework, our
performance metrics can be computed accurately in polynomial-time.
First, we cast the fault diagnosis problem as a sequence of hypothesis tests. At each
time, the performance of a fault diagnosis scheme is quantified by the probability that
the scheme has chosen the correct hypothesis. The resulting performance metrics are
joint probabilities. Using Bayes rule, we decompose these performance metrics into two
parts: marginal probabilities that quantify the reliability of the system and conditional
probabilities that quantify the performance of the fault diagnosis scheme. These conditional
probabilities are used to draw connections between the fault diagnosis and the fields of
medical diagnostic testing, signal detection, and general statistical decision theory.
Second, we examine the problem of computing the performance metrics efficiently
and accurately. To solve this problem, we examine each portion of the fault diagnosis
problem and specify a set of sufficient assumptions that guarantee efficient computation. In
particular, we provide a detailed characterization of the class of finite-state Markov chains
that lead to tractable fault parameter models. To demonstrate that these assumptions enable
efficient computation, we provide pseudocode algorithms and prove that their running time
is indeed polynomial.
Third, we consider fault diagnosis problems involving uncertain systems. The inclusion
of uncertainty enlarges the class of systems that may be analyzed with our framework. It
also addresses the issue of model mismatch between the actual system and the system used
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