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Intrinsic time-scale decomposition and graph signal processing are combined to effectively identify a rotor–stator rubbing fault. The vibration signal is decomposed into mutually independent rotational components, and then, the Laplacian energy index is obtained by the graph signal of the autocorrelation function of rotational components, and the signal is reconstructed by an autocorrelation function of each proper rotation (PR) component relative to smaller Laplacian energy index (less complexity). Finally, characteristics are extracted from rotor–stator rubbing faults in an aeroengine according to square demodulation spectrum of a reconstructed signal. To validate the effectiveness of the algorithm, a comparative analysis is made among traditional intrinsic time-scale decomposition algorithm, combination of intrinsic time-scale decomposition and autocorrelation function, and the proposed intrinsic time-scale decomposition–graph signal processing algorithm. Comparative result shows that the proposed intrinsic time-scale decomposition–graph signal processing algorithm is more precise and effective than the traditional intrinsic time-scale decomposition and intrinsic time-scale decomposition and autocorrelation function algorithms in extracting characteristic frequency and frequency multiplication of rotor–stator rubbing faults and can greatly reduce the number of noise components irrelevant to faults. [ABSTRACT FROM AUTHOR]

• Intrinsic Time-scale Decomposition and Graph Signal Processing is integrated. • A PR component with minimum Laplacian Energy index is chosen. • The ITD-GSP can precisely provide the characteristic frequency of compound faults. • The ITD-GSP algorithm is insensitive to the installation direction of sensors. The diagnosis of compound faults of rolling bearing is extremely difficult due to the nonlinearity and non-stationary of signal. With the purpose of extracting the compound faults from rolling bearings of aero-engine, efforts were made to integrate Intrinsic Time-scale Decomposition (ITD) and Graph Signal Processing (GSP), namely the ITD-GSP methodology. A PR component (obtained by ITD algorithm) with minimum Laplacian Energy (LE) index is chosen as the optimal rotational component to identify types of compound fault of rolling bearing. The result indicates that the proposed ITD-GSP methodology can precisely and effectively provide the characteristic frequency of compound faults no matter in which direction of sensors (vertical and horizontal) and which type of compound faults of rolling bearing. On the contrary, the mainstream schemes of fault analysis using ITD algorithm (correlation coefficients or kurtosis as the basis to screen optimal rotational component) cannot. [ABSTRACT FROM AUTHOR]