ABSTRACT
As discussed earlier, there are two major approaches to fault diagnosis: pattern-based recognition methods and estimation-based methods. Chapter 10 focused on the former. This chapter will discuss the latter method. An estimation-based diagnosis starts with the linear diagnostic model (such as Equation 10.1) and then estimates the variance components for each potential variation source (or random effect) based on the measurement data sample. Knowledge of the variance components, in conjunction with subsequent statistical testing, allows us to assess whether each variation source is present in the current sample and, if present, the severity of the source. Two statistical methods are commonly used in estimating variance components: the least-squares (LS) method (and its variants) and the maximum likelihood (ML) method. In engineering applications, the least-squares methods are more prevalent, perhaps because of its ease of use and quick computation, more suitable for in-line applications. This chapter will present a few variants of LS estimations of variance components. Their interrelationship will be revealed and their performance will be compared. Some convenient tools will be developed to guide the appropriate use of these variance estimators under specific circumstances. This chapter is organized as follows. Section 11.1 presents several variants of LS estimators for variance components. Section 11.2 will discuss the interrelationship among variance estimators. Section 11.3 compares their performances. Section 11.4 summarizes the chapter.
