Vibration signal component separation by iteratively using basis pursuit and its application in mechanical fault detection

Using different transform basis, the vibration signal components, such as impulses, harmonics and modulated components, can be effectively separated by basis pursuit. For multicomponent vibration signals, this paper proposes a new vibration signal component separation approach by iteratively using basis pursuit. The signal is firstly denoised by basis pursuit denoising and the impulsive component can be separated by using identity matrix and redundant Fourier basis. Then signal components with different frequency ranges can be separated by using short-time Fourier transform basis with different window lengths, and the components with high frequency are separated after each iteration. To choose the best basis from the dictionary, the separation coefficient is proposed for evaluating the separating performance of the transform basis. The proposed approach, empirical mode decomposition (EMD) and matching pursuit are respectively applied to analyzing a simulated faulty vibration and a simulated faulty gear vibration signal. The comparison results demonstrate its superiority to EMD and matching pursuit in separation accuracy. Finally, the proposed approach is used for detecting the faults of a rotor and rolling bearings. The results further show that this proposed method can be effectively applied to mechanical fault diagnosis.