Time-varying fault feature extraction of rolling bearing via time-frequency sparsity

• Published in: Measurement science & technology 2021-02, Vol.32 (2), p.25116
• Main Authors: Yi, Cancan, Qin, Jiaqi, Huang, Tao, Jin, Zhangmin
• Format: Article
• Language: English
• Subjects: convex optimization; fault diagnosis; generalized minimax concave penalty; second-order short-time Fourier transform; time-varying feature extraction
• ISSN: 0957-0233; 1361-6501
• DOI: 10.1088/1361-6501/abb50f

The joint time-frequency (TF) distribution is a critical method of describing the instantaneous frequency that changes with time. To eliminate the errors caused by strong modulation and noise interference in the process of time-varying fault feature extraction, this paper proposes a novel approach called second-order time-frequency sparse representation (SOTFSR), which is based on convex optimization in the domain of second-order short-time Fourier transform (SOSTFT) where the TF feature manifests itself as a relative sparsity. According to the second-order local estimation of the phase function, SOSTFT can provide a sparse TF coefficient in the short-time Fourier transform (STFT) domain. To obtain the optimal TF coefficient matrix from noisy observations, it is innovatively formulated as a typical convex optimization problem. Subsequently, a multivariate generalized minimax concave penalty is employed to maintain the convexity of the least-squares cost function to be minimized. The aim of the proposed SOTFSR is to obtain the optimal STFT coefficient in the TF domain for extraction of time-varying features and for perfect signal reconstruction. To verify the superiority of the proposed method, we collect the multi-component simulation signals and the signals under variable speed from a rolling bearing with an inner ring fault. The experimental results show that the proposed method can effectively extract the time-varying fault characteristics.