Detection of weak transient signals based on wavelet packet transform and manifold learning for rolling element bearing fault diagnosis

• A new weak signal extraction method based on wavelet packet transform and nonlinear manifold learning is proposed.
• A different frequency band signal fusion method based on binary wavelet packet transform is proposed to form waveform feature space.
• Minimum permutation criterion is used to select the optimal parameter in the manifold learning algorithm.
• The experimental results validate the effectiveness of the proposed method in weak signature extraction.

The kurtogram-based methods have been proved powerful and practical to detect and characterize transient components in a signal. The basic idea of the kurtogram-based methods is to use the kurtosis as a measure to discover the presence of transient impulse components and to indicate the frequency band where these occur. However, the performance of the kurtogram-based methods is poor due to the low signal-to-noise ratio. As the weak transient signal with a wide spread frequency band can be easily masked by noise. Besides, selecting signal just in one frequency band will leave out some transient features. Aiming at these shortcomings, different frequency bands signal fusion is adopted in this paper. Considering that manifold learning aims at discovering the nonlinear intrinsic structure which embedded in high dimensional data, this paper proposes a waveform feature manifold (WFM) method to extract the weak signature from waveform feature space which obtained by binary wavelet packet transform. Minimum permutation entropy is used to select the optimal parameter in a manifold learning algorithm. A simulated bearing fault signal and two real bearing fault signals are used to validate the improved performance of the proposed method through the comparison with the kurtogram-based methods. The results show that the proposed method outperforms the kurtogram-based methods and is effective in weak signature extraction.