Abstract: In view of the severe shortage of samples for training in mechanical fault diagnosis, a novel method based on graph theory and transductive support vector machine (GTSVM) is presented for gear incipient fault diagnosis. By building a complete graph of original data matrix, a density-sensitive distance is defined to evaluate the dissimilarity between samples, which reflects the data structure well, and the well-known Iris data is used to verify the effectiveness. The vibration signals of gearbox under three running conditions (normal, slight spalling and severe spalling) are analyzed, and 11 time domain features are extracted from original data. Principal component analysis is adopted to select discriminative features, and graph theory is used to process the selected feature sets. Then, transductive support vector machine is trained by gradient descent learning and applied in fault detection and faults classification. The results using GTSVM method are compared with those using support vector machine and transductive support vector machine, which indicates the high classification accuracy of the proposed approach. Besides, the performance in failure detection is also improved through principal component analysis feature selection. Experiments show that the proposed method is effective in gear incipient fault diagnosis.

Key words: Fault diagnosis, Feature selection, Gears, Graph theory, Transductive support vector machine