An Enhanced Trace Ratio Linear Discriminant Analysis for Fault Diagnosis: An Illustrated Example Using HDD Data

This paper proposes a pattern recognition method for the fault diagnosis of machinery based on an enhanced trace ratio linear discriminant analysis (ETR-LDA) algorithm. It is an extension of TR-LDA that pursues to maximize the between-class distance and minimize the within-class distance. Since TR-LDA focuses on the total between-class distance and ignores the attention to local features, it may lead to deficiencies in the classification of specific patterns/classes, which is defined as short board in this paper. To cope with this limitation, the proposed ETR-LDA makes a reconsideration of the relationship between the total between-class distance and the global separability. More specifically, a new objective function is derived in ETR-LDA by taking the smallest between-class distance into account. The optimal solution of this objective function is proved to improve the smallest between-class distance with no change to the convergence and the global optimality of the algorithm, and the separability of different classes is increased eventually. Both synthetic data and hard disk drive wearing experimental data are employed to verify the efficiency of the proposed method. The results show that ETR-LDA is able to distinguish those fault categories and outperform TR-LDA and other dimensionality reduction methods.