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To solve  the problem  that  the  random distribution of noise  in  the  time‐frequency  (TF) plane largely affects the readability of TF representations, a novel signal adaptive decomposition algorithm processed in TF domain, which provides adequate information about the time‐varying instantaneous frequency, is presented in this paper. The theoretical basis of this algorithm is short‐ time Fourier transform (STFT). The research into the algorithm comprises two steps: the TF plane denoising  takes  sparse  low‐rank  matrix  estimation  as  a  priority  and  then  achieves  signal decomposition  based  on  reassignment  vector  (RV). A  low‐rank matrix  approximation  scheme, which  exploits  the  sparse  properties  of  the  TF  transformation  coefficient  and  uses  non‐convex penalty, is put forward to obtain clean STFT. Then, a new approach called RV, which is different from the traditional mode decomposition methods such as Empirical Mode Decomposition (EMD), is used to estimate the characteristic curve corresponding to the TF ridges of the interested modes. Based on  the classical reassignment method, RV has a solid  theory  foundation. Moreover,  it can identify  different  signal  components  such  as  stationary  signal, modulating  signal  and  impulse characteristic. Combining the advantages of low‐rank matrix approximation approach and those of RV defined in TF plane, a novel signal adaptive decomposition method is proposed in this paper to identify  fault characteristics. To  illustrate  the effectiveness of the method,  fault signals of rolling bearing under stationary condition and time‐varying speed are respectively analyzed.

A Novel Adaptive Mode Decomposition Method Based on Reassignment Vector and Its Application to Fault Diagnosis of Rolling Bearing