A Family of Health Indicators Induced by EOF for Condition Monitoring of Machinery

The performance of bearing approximately satisfies ergodicity property, therefore, investigating it in the spatiotemporal domain is theoretically feasible. This article pioneers the application of empirical orthogonal functions (EOF) from meteorological analysis and forecasting to the intelligent maintenance field of rotating machinery. First, a Hankel matrix is constructed using a column vibration signal, then we use EOF for the Hankel matrix to gain a time matrix, a space matrix, and a contribution rate vector. Second, some indicators are constructed based on the time matrix, whereas a brand-new spatiotemporal indicator is designed based on contribution rate vector. By calculating the total contribution rate and selecting some vectors in time and space matrices, the reconstructed signal can be obtained, and then some other indicators are constructed using the reconstructed signal. This article addresses two main challenges: first, decreasing the effect of noise, thus improving the ability to detect early failure in complicated environment; second, separating vibration signals into mutually orthogonal quantities in time-space perspective. The proposed method is validated on two bearing datasets, and the results show that the proposed indicators can either reflect the early defect or assess the degradation trend. Among all indicators, the brand-new designed indicator in spatiotemporal domain achieves the two goals simultaneously: when the early failure occurs, the indicator indicates a huge change, and with the further degradation of the bearing health state it remains good monotonicity and trend. Therefore, the designed health indicators enrich the family of statistical health indicators for machinery.