Intelligent fault diagnosis for rotating machinery using L1/2-SF under variable rotational speed

Sparse filtering (SF), as an effective feature extraction technique, has attracted considerable attention in the field of mechanical fault diagnosis. But the generalization ability of SF to handle non-stationary signal under variable rotational speed is still poor. When the rotating parts of mechanical transmission work at a constant speed, the collected vibration signal is strongly correlated with the fault type. However, the mappings will no longer be so simple under the condition of variable rotational speed, which brings a rigorous challenge to intelligent fault diagnosis. To overcome the aforementioned deficiency, a novel L-1/2 regularized SF method (L-1/2-SF) is studied in this paper. Specifically, L-1/2 regularization strategy is added to the cost function of SF, then the L-1/2-SF is directly employed to extract sparse features from the raw vibration data under variable rotational speed condition. In order to understand the sparse feature extraction ability of the L-1/2 regularization, a physical explanation of the sparse solution generated by the L-1/2 regularization strategy is explored. Next, softmax regression is employed for fault classification connected with the output layer of L-1/2-SF. The effectiveness of L-1/2-SF method is verified using a planetary gearbox dataset and a bearing dataset, respectively. Experiment results show that L-1/2-SF can deal well with the variable rotational speed problem and is superior to other methods.