Wavelet-based denoising methods are very popular at present [5�C13]. However, some problems still remain. For instance, it is hard to select the optimal wavelet basis for signal denoising to avoid the loss of useful components in the signal, and there is no unique and effective method to choose the threshold value in discriminating the noise. The TFA has the merit that it can intuitively represent the time-frequency information in a two-dimensional domain, so it can be used to maintain good time-frequency properties in denoising. One of typical methods is the short-time Fourier transform (STFT) threshold denoising (also called spectrum subtraction), which has been popularly used for speech signal denoising [14]. There are still some remaining issues to be studied for this method, which makes the denoising effect unsatisfactory in complex noise background situations.

A time-frequency domain averaging method to clean up the noise by calculating the geometric average in the time-frequency domain for a strictly periodic vibration signal was reported in [15]. There is also a study addressing threshold denoising in the reconstruction of a composite dictionary (combining impulse time-frequency dictionary and Fourier dictionary) multi-atom matching decomposition [16]. In the TFA-based denoising approach, one of the most important issues is how to correctly distinguish noise in the time-frequency domain.Recently, we have proposed a time-frequency manifold (TFM) technique [17], which has the potential to solve the problem in TFA-based denoising approach.

The TFM combines the benefits of TFA in representing the non-stationary information and manifold learning in extracting the intrinsic nonlinear structure of high-dimensional data, so it has merits in noise suppression and resolution enhancement in the time-frequency domain. The merits of the TFM benefit signal denoising based on the TFA approach [18]. We have thus proposed a TFM-based signal denoising method for a better machinery fault signal reconstruction [18]. The basic idea of this method is to synthesize a clear fault signal from the TFM signature of the raw signal. As the TFM is a time-frequency structure with a high resolution for representing impulse components of interest and excellent suppression effect for the noise, theoretically the signals reconstructed from the TFM will have satisfactory denoising effects.

This paper further develops the TFM-based data denoising method in a systematic way, and addresses the utility of this method for effective fault diagnosis. Specifically, the TFM signature is learned by combining the top two TFMs in this study. The synthetic signature will have a better denoising effect in the time-frequency GSK-3 domain. Moreover, the TFM-based data denoising method is evaluated by introducing a clustering-based statistical parameter by considering the merit of TFM.