Novel Gauss-Hermite integration based Bayesian inference on optimal wavelet parameters for bearing fault diagnosis

Dong Wang, Kwok Leung Tsui, Qiang Zhou

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Rolling element bearings are commonly used in machines to provide support for rotating shafts. Bearing failures may cause unexpected machine breakdowns and increase economic cost. To prevent machine breakdowns and reduce unnecessary economic loss, bearing faults should be detected as early as possible. Because wavelet transform can be used to highlight impulses caused by localized bearing faults, wavelet transform has been widely investigated and proven to be one of the most effective and efficient methods for bearing fault diagnosis. In this paper, a new Gauss-Hermite integration based Bayesian inference method is proposed to estimate the posterior distribution of wavelet parameters. The innovations of this paper are illustrated as follows. Firstly, a non-linear state space model of wavelet parameters is constructed to describe the relationship between wavelet parameters and hypothetical measurements. Secondly, the joint posterior probability density function of wavelet parameters and hypothetical measurements is assumed to follow a joint Gaussian distribution so as to generate Gaussian perturbations for the state space model. Thirdly, Gauss-Hermite integration is introduced to analytically predict and update moments of the joint Gaussian distribution, from which optimal wavelet parameters are derived. At last, an optimal wavelet filtering is conducted to extract bearing fault features and thus identify localized bearing faults. Two instances are investigated to illustrate how the proposed method works. Two comparisons with the fast kurtogram are used to demonstrate that the proposed method can achieve better visual inspection performances than the fast kurtogram.

Original languageEnglish (US)
Pages (from-to)80-91
Number of pages12
JournalMechanical Systems and Signal Processing
StatePublished - May 1 2016
Externally publishedYes


  • Bayesian inference
  • Bearing fault diagnosis
  • Gauss-Hermite integration
  • Kurtogram
  • Wavelet transform

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


Dive into the research topics of 'Novel Gauss-Hermite integration based Bayesian inference on optimal wavelet parameters for bearing fault diagnosis'. Together they form a unique fingerprint.

Cite this