The vibration signal of rotating machinery fault is a periodic impact signal and the fault characteristics appear periodically. The shift invariant K-SVD algorithm can solve this problem effectively and is thus suitable for fault feature extraction of rotating machinery. With the over-complete dictionary learned by the training samples, including thedifferent classes, shift invariant sparse feature for the training as well as test samples can be formed through sparse codes and employed as the input of classifier. A support vector machine (SVM) with optimized parameters has been extensively used in intelligent diagnosis of machinery fault. Hence, in this study, a novel fault diagnosis method of rolling bearings using shift invariant sparse feature and optimized SVM is proposed. Firstly, dictionary learning by shift invariant K-SVD algorithm is conducted. Then, shift invariant sparse feature is constructed with the learned over-complete dictionary. Finally, optimized SVM is employed for classification of the shift invariant sparse feature corresponding to different classes, hence, bearing fault diagnosis is achieved. With regard to the optimized SVM, three methods including grid search, generic algorithm (GA), and particle swarm optimization (PSO) are respectively carried out. The experiment results show that the shift invariant sparse feature using shift invariant K-SVD can effectively distinguish the bearing vibration signals corresponding to different running states. Moreover, optimized SVM can significantly improve the diagnosis precision.

For mechanical compound fault, it is of great significance to employ the vibration signal of a single-channel compound fault to analyze and realize the separation of multiple fault sources, which is essentially the problem of single-channel blind source separation. Shift invariant K-means singular value decomposition (shift invariant K-SVD) dictionary learning is suitable to extract the periodic and repeated fault features of a rotating machinery fault, hence in this article a single-channel compound fault analysis method is put forward which combines shift invariant K-SVD with improved fast independent component analysis (improved FastICA) algorithm. Firstly, based on single-channel compound fault signal, the shift invariant K-SVD algorithm can be used for learning multiple latent components that can be constructed as a virtual multi-channel signal. Then the improved FastICA algorithm is utilized to realize the separation of multiple fault source signals. With regard to the FastICA algorithm, the third-order convergence Newton iteration method is adopted to improve convergence speed. Moreover, in order to address the problem that FastICA is very sensitive to initialization, a steepest descent method can be applied. The experimental analysis of the compound fault of rolling bearing verifies that the presented method is effective to separate multiple fault source signals and the improved FastICA algorithm can increase convergence rate and overcome the problem of sensitivity to initialization.

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