A Novel Variable Convolution Kernel Design According to Time-frequency Resolution Altering in Bearing Fault Diagnosis

Timely diagnosis of bearing faults can effectively predict initial faults and avoid severe accidents. Ordinary neural networks have achieved relatively high accuracy for bearing failure classification. However, for the convolution process in neural networks, convolution kernels of fixed size are used across the whole image acquired by the time-frequency transformation, which is prone to overlook the intrinsic local time-frequency features of data. So as to solve this problem that the kernel may not reflect the local time-frequency characteristics of the non-stationary signal, a new method for planning convolutional kernels is proposed in this paper. We leverage variable kernels to capture the time-frequency resolution altering nature within the non-stationary signals. Firstly, starting from the time-frequency characteristics of non-stationary signals, the theoretical basis of adopting variable convolution kernels is analyzed, and the impact of Heisenberg's measurement inaccuracy principle on the design of the learning framework is analyzed in-depth with wavelet analysis as an example. Secondly, since the performance of different wavelet basis functions on time-frequency resolution varies dramatically, after comprehensive study of the mutual relationship between these resolutions, a proper criteria is deduced to deliver the measurement of performances, and the Gabor wavelet basis is chosen according to this principle. This design can be obtained by using wavelet analysis parameters before learning and training. This method is orthogonal to the model training process and can be plug-and-play with other deep learning frameworks. Finally, it is shown through datasets and practical experiments that the proposed method outperforms other newly proposed classification methods in terms of achieving higher accuracy in less time.