Low-dimensional multi-scale Fisher discriminant dictionary learning for intelligent gear-fault diagnosis

Fisher discriminant dictionary learning (FDDL) is an effective classification method that has achieved excellent results in image processing. However, there are still some shortcomings when it is directly applied to intelligent gear-fault diagnosis, such as low classification accuracy, a time-consuming dictionary learning process and unsatisfactory anti-interference capabilities, especially for vibration signals with heavy noise. To solve these problems, this paper proposes a low-dimensional multi-scale FDDL (LM-FDDL) model, which extracts the fault-sensitive and multi-scale information from wavelet packet transform coefficients, and constructs a low-dimensional sample set via L-kurtosis for dictionary learning. This improves the anti-interference capability of the model and greatly reduces the computational cost. The dictionary learned from the low-dimensional sample set has excellent discriminant performance and interpretability, which are verified by the visualization of reconstructed signals. Experimental results for a spur-gear fault dataset and a bevel-gear fault dataset demonstrate the superiority of LM-FDDL over other related methods in terms of fault classification accuracy and computational cost. An added-noise comparison experiment verifies that the dimension-reducing strategy of LM-FDDL has strong robustness to noise and outliers, and thus ensures that the main fault features can be extracted from vibration signals with heavy noise interference.