Fractional Fourier and time domain recurrence plot fusion combining convolutional neural network for bearing fault diagnosis under variable working conditions

The dependence on big data and lengthy training time discount the advantages of deep learning methods applied in machinery fault diagnosis. Moreover, the performance of deep models will degrade due to the inconsistency of fault data collected under variable working conditions. In this paper, we introduce a novel data representation based on fractional Fourier transform (FRFT) and recurrence plot transform that can give full play to convolutional neural networks (CNN) to achieve bearings fault diagnosis with limited data amount, where FRFT plays the role of feature extractor by generating fractional Fourier spectrum with maximum kurtosis, and recurrence plot serves as visualization tool for texture features in time domain and fractional Fourier domain. Experimental results indicate that CNN trained by FRFT based recurrence plot outperforms Fourier spectrum derived recurrent plot and short time Fourier transform based time-frequency spectrum, moreover, the best performance can be achieved when maximum kurtosis based fractional Fourier domain recurrence plot is fused with time domain recurrence plot, as CNN trained by fused images can be adaptive to the changes of rotating speed and working load. The proposed method offers a promising tool for bearing fault diagnosis under variable working conditions and could be extended to other applications.