Inference and Quantification of Cyclostationary Impulses: A novel noise-sensitive mixed Gaussian cyclostationary model for compound fault detection

Rolling bearings are fundamental components in modern industrial systems, where real-time fault diagnosis is vital for enhancing operational safety and optimizing maintenance strategies. Traditional signal demodulation and blind deconvolution techniques are often designed to extract a single cyclostationary impulse with periodic statistics from single fault signals by filtering. However, they cannot provide quantitative confidence levels for diagnosis results, and nonlinear filtering often disrupts multiple local periods on statistics, called the quasi- and pseudo-cyclostationary properties, in handling compound fault signals. This study proposes a novel noise-sensitive mixed Gaussian cyclostationary (MGC) model, designed to model multiple cyclostationary impulses in compound fault signals under noisy conditions. Statistical derivation demonstrates that it can model and demodulate noise- and impulse-coupled systems with probabilistic, additive, and multiplicative coupling. Additionally, a standardized fault diagnosis process is proposed, using spectral correlation analysis to test the existence of cyclostationary and developing progressive likelihood ratio testing to accurately select the optimal cyclostationary period combinations for MGC modeling and compound fault diagnosis. Without the need to compare with normal signals, the method provides a quantitative statistical confidence level for diagnosis results. Extensive simulations and comparative experiments demonstrate that the method can more accurately extract different cyclostationary impulses from various compound fault combinations.