_applied sciences_  
_Article_  
A Novel Strategy for Signal Denoising Using Two-Layer SVD and Its Application to Rub-Impact Fault Diagnosis of Aeroengine \({}^{\ddagger}\)  
[PERSON] 1,2, [PERSON] 1,*, [PERSON] 1,*, [PERSON] 1,*,*, [PERSON] 2, [PERSON] 2, [PERSON] 2 and [PERSON] 2  
1 College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 20106, China; [PERSON]L_ADDRESS].com  
2 AECC Guiyang Engine Design Research Institute, Guiyang 550081, China; [EMAIL_ADDRESS] (K.Z.); [EMAIL_ADDRESS] (M.S.); [EMAIL_ADDRESS] (J.T.); [EMAIL_ADDRESS] (X.Y.)
* Correspondence: [EMAIL_ADDRESS] (S.L.); [EMAIL_ADDRESS] (K.X.); [EMAIL_ADDRESS] (S.G.); Tel.: +86-1360519967 (S.L.); +86-1364216687 (K.X.); +86-13695981968 (S.G.)
* Part of the content of this article was published at the \"The 12 th IEEE Global Reliability & Prognostics and Health Management Conference (HEPM Nining 2021)\", and this article has been expanded on the basis of the conference paper. [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A Novel Strategy for Signal Denoising Using Two-Layer SVD and its Application to Rub-impact Fault Diagnosis of Aero-engine, In Proceedings of the IEEE Global Reliability & Prognostics and Health Management Conference, Nanjing, China, 15-17 October 2021. The main changes include: 1. The addition of two sets of data regarding low-pressure turbine species, these are 6660 r/min and 5220 r/min, respectively. To process these data, the following method was proposed. 2. To decompose the signal into several components, the Variational Mode Decomposition was used, instead of a filter. 3. In the previous conference paper, the time-frequency diagram obtained by the proposed method and the time-frequency diagram obtained through Hilbert-Huang transform were not in the same figure, so it was not convenient to compare them. In the present study, they are placed in the same figure, and the relevant content is placed above this figure. 4. The time-frequency diagram of data using short-time Fourier transform and variational nonlinear chirp mode decomposition was added. 5 Additional information, including: \"At some rotation speeds, the fluctuating frequencies of the instantaneous frequencies are consistent with the fluctuating frequencies on the scope spectrum\" and 6 \"by comparing several methods with rub-impact fault data without denoising, when only 1\(\times\) is decomposed, the proposed method, HHT, and VNCMD can all obtain time-frequency representations of 1\(\times\), and the waveform of instantaneous frequency of 1\(\times\) obtained by the proposed method is better at this time. When it is necessary to decompose 1\(\times\) and 3\(\times\), only the proposed method can successfully obtain time-frequency representation of 1\(\times\) and 3\(\times\).\" were added in the last chapter. 7 Four references have also been added.  
**Abstract:** The rub-impact fault, which occurs in the aeroengine, can cause frequency modulation (FM) in its vibration signal. Oscillated instantaneous frequency (IF) is a phenomenon of such a modulation mode, which carries critical fault information from the aeroengine. In this paper, by using Variational Mode Decomposition (VMD), the vibration signal can be decomposed into several signal components. Two-layer Singular Value Decomposition (SVD) is utilized to reduce the signal noise of each signal component and instantaneous frequency of each signal component. The intra-wave FM feature of the signal are presented through the Hilbert transform (HT) analysis. The proposed method is validated with numerical simulation and then demonstrated on aeroengine data with the rub-impact fault. The proposed method is suitable for the analysis of modulated signals and is a valid tool for detecting the rub-impact faults in aeroengines.  
**Keywords:** aeroengine; singular value decomposition; two-layer singular value decomposition; frequency modulation