Low-Rank Informed Adaptive Chirp Mode Decomposition and Its Application in Rotating Machine Fault Diagnosis Under Varying Speed Conditions

Diagnosing faults in rotating machines under varying speed conditions is challenging because of nonstationary and intricate time-varying characteristics of vibration signals. Accurate fault diagnosis requires the precise extraction of time-varying information, especially instantaneous frequencies (IFs). The adaptive chirp mode decomposition (ACMD) demonstrates significant capability and adaptability in decomposing nonstationary multicomponent signals into multiple modes and capturing the time-varying characteristics of each mode, but it overlooks the inherent proportional relationship among IFs in rotating machine vibration signals (RMVSs). This limitation hampers its effectiveness in processing such signals, particularly in scenarios with closely spaced IFs and significant noise levels. To address this limitation, this article proposes the low-rank informed ACMD (LRACMD), which leverages the proportional relationship by imposing a low-rank (LR) constraint. To be specific, it is first revealed that the proportional relationship of IFs can be effectively characterized by constraining LR property. Then, the LR optimization problem and its solving algorithm are introduced to impose this constraint. Moreover, the LR constraint is embedded into the IF update process of the ACMD, resulting in the development of LRACMD. Both simulation and experimental results indicate that the LRACMD estimates the IFs of signals more accurately than several comparative methods and successfully identifies the bearing and gear faults in varying speed conditions, thereby confirming its effectiveness and robustness.