Methodology for health indicators design based on distributions’ distance measures applied to robust CSC maps. Application to non-Gaussian vibration-based fault detection

We address the problem of vibration-based local damage detection in rolling element bearing in the presence of non-Gaussian noise. The main challenge is to design a health indicator (HI) that efficiently detects damage at an early stage. Classical time domain statistical approaches, such as kurtosis or second order cyclostationarity-based health indicators, often fail due to the presence of large, non-cyclic outliers. Our methodology is based on cyclostationary analysis using the cyclic spectral coherence (CSC) map. Due to presence of non-Gaussian noise, recently developed robust CSC maps are considered (trimmed covariance- and Spearman correlation-based estimators). The empirical distributions of the samples from informative and non-informative parts of the maps are calculated and distance between such distributions is estimated. This distance could be interpreted as “difference” between distributions, and the progressing fault should increase this distance. Two scenarios for distributions’ distance calculations are proposed. They are based on the empirical distribution function and kernel density estimator. In the first scenario, we apply the Kolmogorov–Smirnov and Cramer test statistics while in the second one, the Hellinger and the Jeffreys distances. To validate the results, the monotonicity, the trendability, and the prognosability criteria are used for simulated data. For real data, when only one HI curve is available, we proposed a method that focuses on the separability (between healthy and faulty conditions) evaluated using the Fisher criterion. For the second real dataset, where only signals from healthy and faulty states were available, we proposed comparing the ratio between HIs derived for these two states. Our results outperform raw signal-based and classical CSC-based HIs. • New methodology for health indicators design is proposed. • Robust CSC maps are utilized. • Distribution of samples from CSC map are derived. • Distributions’ distance measures are proposed as a new HI. • Simulated and real data are used for validation.