A discussion on the differences between the cyclic spectral correlation and coherence for cyclostationarity-based condition monitoring

Vibration signals measured on rotating machinery typically exhibit cyclostationarity due to the inherent nature of real-world rotating vibration sources. Hence, the development of signal processing tools devoted to investigating or exploiting this cyclostationarity for condition monitoring purposes of gears and bearings has seen a significant increase in research interest. One of the main approaches to analyze a vibration signal’s cyclostationary behavior is the cyclic spectral correlation and its normalized derivative, the cyclic spectral coherence. Even though these two methods are closely related, they do offer different statistical insights which may influence the fault detection and trending capabilities of these tools. The aim of this work is to investigate the performance of these two methods with regard to the accuracy of tracking mechanical degradation over time. The normalization of the spectral coherence, which makes it independent of the signal power spectrum, improves the interpretability of the resulting coherence spectrum but it may lead to suppress or equalize fault-related frequency bands relative to other frequency bands and it may skew the coherence spectrum amplitudes of fault harmonics in different operating regimes for complex machinery. Tracking the evolution of a second-order cyclostationary component over time might thus be hindered by this normalization, which can lead to issues when combining such a tool with a data-driven machine learning technique that employs the operating conditions for making the cyclostationary indicators operating condition independent. Instead, using the cyclic spectral correlation, which is not normalized, may provide a more accurate depiction of the degradation process. This paper investigates whether there is any significant benefit to using the cyclic spectral correlation over the cyclic spectral coherence for monitoring complex rotating machinery and if so, when it makes sense to prefer one over the other. To answer these questions, both simulated and experimental vibration data is examined in order to highlight the differences between the two concepts.