Distance-based analysis of dynamical systems reconstructed from vibrations for bearing diagnostics

Nonlinear fault responses are common in industrial systems yet cannot be effectively extracted by traditional feature extraction methods. In recent years, more techniques based on nonlinear dynamical system reconstruction are reported in the fault diagnosis and prognosis context. However, the key phrases researchers used vary from area to area, and it is difficult to locate the relevant papers. In this paper, we connect the related bearing fault diagnostics and prognostics literature in a short review. We propose a method for reconstructing dynamical system based on time-delay embedding and use it on bearing fault diagnostics. Based on one Wasserstein distance, the earth mover's distance (EMD), we compare the reconstructed bearing vibration data with a baseline reconstruction from normal (healthy) bearing data to generate a severity index over time. Fault type assessment is performed by visualizing the distances between different reconstructed dynamical systems in a two-dimensional plot of the multidimensional scaling (MDS) results. We illustrate the proposed method with two laboratory bearing degradation datasets. We compare the trend with statistical features obtained from time and frequency domain, as well as the EMD trend without using phase space reconstruction. The EMD of reconstructions shows large difference between incipient faults and normal data, and then decreases to the normal bearing level. The EMD ratio is proposed as a fault severity indicator based on shape similarity information not available in the raw data features. The MDS results provide good visualization of the distances among time series for clustering and fault type diagnosis.