Accurate decomposition of complex multi-component nonstationary signals of rotating machinery: A novel polynomial chirp mode decomposition approach

• We propose a novel signal decomposition method called PCMD. • PCMD has established a new IF estimation method called APIFO based on PCT. • PCMD proposes a new signal mode reconstruction scheme called IACTF. • PCMD proposes an IA correction strategy for signals with crossing IFs. • Experiments show that PCMD can accurately decompose complex nonstationary signals. In complex operating environments, the monitoring signals of rotating machinery often exhibit significant nonlinearity and non-stationarity, which creates major challenges for fault diagnosis. Although adaptive chirp mode decomposition (ACMD) offers high time–frequency resolution, its performance deteriorates with inaccurate initial instantaneous frequency (IF) estimation and shows limitations when processing signals with crossing IFs. To address these issues, this paper proposes a novel polynomial chirp mode decomposition (PCMD) method to enhance decomposition accuracy for complex multi-component signals. Firstly, we propose an adaptive IF optimization scheme (APIFO) based on the polynomial chirplet transform (PCT), which adaptively determines the fitting order of PCT in accordance with the error-adjusted R-Squared value to achieve accurate estimation of the IF. Secondly, based on demodulation techniques, we introduce an instantaneous amplitude (IA) chirp tracking filter to reconstruct the signal modes and extract the IA using the IF provided by APIFO. Finally, we propose an IA correction strategy for signals with crossing IFs. This strategy first classifies the signal modes by the absolute value of the second derivative of IA and then corrects the modes of different categories through weighted fitting or LSTM neural network methods. Simulation and experimental results demonstrate that the PCMD method provides superior IF estimation and accurate mode decomposition performance compared with classical techniques in rotating machinery fault diagnosis applications.