Fault Detection Statistics Research Articles

Numerical linear algebra in the integrity theory of the Global Positioning System

The Global Positioning System (GPS) is a satellite based navigation system. Since safety is the main concern for aircraft navigation, various means of monitoring the integrity (certainty of position) have been developed. This is an important area of research in the GPS community. In the following, it will be shown how some numerical linear algebra techniques can be applied to this interesting application. A typical model is presented. A uniform approach to derive the statistics for fault detection and isolation by orthogonal transformations is given. It is shown that the diagonal elements ω ii 2 of the orthogonal projection matrix onto the residual space are fundamental to the theory and understanding of integrity. ω ii can, for example, have a drastic effect on integrity when they are small. The sensitivity of related problems in this area are discussed.

HIGHER-ORDER TIME–FREQUENCY ANALYSIS AND ITS APPLICATION TO FAULT DETECTION IN ROTATING MACHINERY

Impulsive acoustic and vibration signals within rotating machinery are often induced by irregular impacting. The detection of these impulses can be useful for fault diagnosis purposes. Recently there has been an increasing trend towards the use of higher-order statistics for fault detection within mechanical systems based on the observation that impulsive signals tend to increase the kurtosis values. This paper considers the use of the third- and fourth-order Wigner moment spectra, called the Wigner bi- and tri-spectra respectively, for analysing such signals. Expressions for the auto- and cross-terms in these distributions are presented and discussed. It is shown that the Wigner trispectrum is a more suitable analysis tool and its performance is compared to its second-order counterpart for detecting impulsive signals. These methods are also applied to measured data sets from a car engine and an industrial gearbox.