Research of bearing fault diagnosis methods based on persistent homology

The persistent homology method is a recent big data analysis tool that can not only explore the nonlinear structure of high-dimensional complex data but also discover the shape of the data. In this article, a sliding window method is used to construct point clouds from Case Western Reserve University mechanical vibration signal sequences, and Vietoris-Rips (VR) complex filtration models are established based on the point clouds. The persistent homology method is used to extract intrinsic topological features from original vibration signals based on the VR complex filtration models; the topological features include persistent barcode plots and Betti curves. The topological features of the signals are treated as 2D images and fed into the GoogleNet transfer learning model. The classification for each load, prediction for different loads, and prediction for different damage diameters in the sample data are performed separately. We compare the VR complex filtration models with the traditional continuous wavelet transform model and other latest methods and find that they each have their own advantages. Different partitioning methods of the dataset are adopted to obtain various point clouds (sample data) in this article; the partitioning methods for potential data leaks are compared with those without data leaks, and their impacts on the diagnostic results are described. All experimental results are obtained on independent test sets, and the experimental results are authentic and effective, avoiding the problem of data leakage during the experimental processes. By extracting intrinsic similar topological features from the source and target domains using the VR filtration models, the experimental results show that the models have good performance on bearing fault diagnosis in both single-source and multi-source domains. Especially, our proposed models have reliable diagnostic ability for smaller datasets, and they possess good robustness and generalization.