A variant fisher discriminant analysis algorithm and its applicationto fault diagnosis

In order to improve the discriminant power, a new discriminant analysis algorithm is proposed based on Fisher´s linear discriminant, called variant fisher discriminant analysis with orthogonal discriminant components (VFDAODC). The basic idea of the proposed VFDAODC is to overcome the problems of the conventional fisher discriminant analysis algorithm. First, a two-step feature extraction procedure is implemented to avoid the singular problem of within-class scatter matrix for the eigenvalue decomposition. Also, considering that the number of extracted discriminant components is limited by rank deficiency of the between-class scatter matrix, an iterative feature extraction procedure is implemented which can extract as many components as the rank of the within-class scatter matrix. Besides, to guarantee the orthogonality of discriminant components for each class, data deflation is performed within each class of data set whenever a discriminant component is extracted. Using the proposed algorithm, its applications to fault diagnosis are studied. In comparison with the conventional FDA algorithm, the proposed algorithm can better separate different classes and thus provide more promising fault diagnosis performance, revealing its effectiveness.