Integrated Bearing Condition Monitoring and Fault Diagnosis via Distribution-Adaptive Composite Correlation Under Mixed Gaussian–Laplace Noise

Bearing condition monitoring is essential in ensuring the reliable operation of machinery. Yet most vibration-analysis techniques implicitly assume Gaussian noise—a premise often violated in practice, where signals contain Laplace components or Gaussian–Laplace mixtures. To overcome this limitation, we propose a Distribution-Adaptive Composite Correlation (DACC) framework that simultaneously performs condition monitoring and early fault diagnosis under mixed Gaussian–Laplace noise. First, the classical noise-resistant correlation (NRC) is generalized to remain robust against heavy-tailed Laplace disturbances and broadband Gaussian interference. This generalized NRC is fused with the frequency-domain energy ratio to form a composite correlation that accentuates fault-related impulses while suppressing stochastic fluctuations. Integrating the composite correlation over a sliding window yields a scalar health index that evolves monotonically with bearing degradation. An exponentially weighted moving-average (EWMA) chart is then applied to track this index to indicate incipient anomalies. Experiments on simulated signals with pure Laplace, and Gaussian-Laplace mixed noise, as well as on public bearing datasets, show that DACC detects degradation earlier and with lower false-alarm rates than state-of-the-art methods, demonstrating its effectiveness for integrated bearing-condition monitoring and fault diagnosis in practical applications.