Automatic fault diagnosis of rotating machines by time-scale manifold ridge analysis
Introduction
Analysis of vibration or acoustic signals from mechanical systems is widely used in the area of machinery fault diagnosis. The measured signals from a rotating machine usually have the non-stationary property due to varying operation conditions and possible faults inside the machine. Moreover, the dynamic characteristics of measured signals are always non-linear because the mechanical system itself is non-linear. In addition, the noise is inevitably involved in the observed signals in a complex working environment. Therefore, a good signal analysis method should represent the non-stationary characteristics and reveal the intrinsic non-linear dynamics, as well as enhance the weak fault information buried in severe background noise.
As an effective approach of analyzing non-stationary signals, the TFA can convert a one-dimensional time series to a two-dimensional TF representation known as the TFD. The TFD can represent the frequency characteristics which are varying with time, and thus provide a good representation for transient signals carrying fault information. Conventional TFA methods include the STFT [1], the CWT [2], [3] and the WVD [4]. Each of them has its own merits as well as deficiencies, which make it suitable only for specific signals [5]. For example, the STFT is suitable for the signal which is piecewise stationary at the scale of the selected window width. The CWT is particularly suitable for the signal containing transient impulsive components, as well as different frequency components at different scales such as fractal signals. The WVD is very useful for mono-component signals with the merit of excellent TF concentration without any cross-terms. To improve the performance of traditional TFDs, there have emerged several other TFA methods in the field of machinery fault diagnosis. Improving the TF resolution is one key evolution to break the restriction of the Gabor–Heisenberg inequality [6] from which conventional TFA techniques suffer. The ITFS is an improved TFD with better resolution both in time domain and in frequency domain by displaying the IF and the IA on the TF plane after the EMD [7], [8] or LMD [9], [10]. The reassignment of TFD is another technique to produce a better concentration of fault-induced impacts by moving the components from the geometrical center of the TF window to the gravity center of this local domain, which provides much more representative result of the local energetic distribution of the signal [11], [12], [13]. Moreover, by the fusion techniques of different TFDs of the inspected signal, the representations with high resolution on the TF domain can be preserved, while the interference components are rejected, which forms a more accurate TFD [5], [14]. However, for all the TFA methods above, there is no effective approach to deal with the corruption by the heavy noise contained in the signal. For the noise-contaminated signal, de-noising is another target to be solved for the TFA methods. A TFDA method is reported to clean up the noise by calculating the geometric average in the TF domain for a periodic vibration signal [15]. But this method is limited to the strict periodic property for the faulty impacts of the analyzed signal. In addition, the TF spectrum of HWT is constructed to eliminate the interference components outside the fault-contained frequency band, due to the ideal band-pass filtering effect of the harmonic wavelet [16]. But the noise inside the fault frequency band still exists. Most recently, He et al. [17] proposed a novel signature called TFM for machine fault signature representation. By the TFM technique, the inherent fault-related TF structure of the non-stationary signal can be well extracted, and at the same time, the chaotic noise is discarded completely, which exhibits perfect effect of de-noising in the TF domain.
The vibration signal from a rotating machine is usually in the form of AM or FM when a fault occurs. Therefore, the demodulation techniques are usually introduced to identify the fault characteristic frequency. The fault components can be demodulated from either the time domain, or the TF domain. HT is the most common time-domain demodulation method by extracting the envelope of the vibration signal. For the enveloping method, a band-pass filter is needed to firstly capture the modulated high-frequency carrier components (e.g., structural resonance frequency) of the signal. Except for the traditional digital filters, the EMD and WPT were also introduced as band-pass filters [6], [18]. The kurtogram [19], sparsogram [20] and protrugram [21] were proposed successively for the design of optimal frequency band for band-pass filtering. By whatever means, only the noise outside the selected frequency band is removed from the original signal, while that inside the selected frequency band cannot be wiped off yet in the Hilbert envelope. The TF-domain demodulation techniques can present the demodulated components on the TF plane intuitively without the selection of filtering band, thus are appropriate for demodulating the components with a wider frequency span in the TF domain. The ITFS introduced above is a kind of TF-domain demodulation method. However, the demodulated fault information lies on the TF plane and is identified only by visual inspection. Wavelet ridge is a curve appearing in the time-scale plane after the CWT with most of signal energy being concentrated [22]. It contains crucial physical information and has been employed as another TF-domain demodulation approach for fault diagnosis of rotating machines [23]. By this approach, the FM and AM components corresponding to the fault can be directly identified in the spectrum of the computed IF and IA from the wavelet ridge, respectively.
This paper explores the improved TF representation by considering the non-linear property in the de-noising sense for effectively identifying the fault characteristic frequency in the TF domain. Specifically, a new signature, called TSM, is proposed for a better representation of machinery fault pattern, and then the TSM ridge is extracted in the time-scale plane as a new demodulated result to identify the precise fault frequency. The TSM is produced by a combination of the CWT and manifold learning. It is natively a kind of improved TFD since the scale and the frequency are interconvertible. For the TSM generation, an optimal scale band is selected to eliminate the influence of unconcerned scale components, and the noise in the selected band will be removed by manifold learning to highlight the inherent non-linear structure of faulty impacts. The TSM ridge is further extracted by minimizing the cost functions step by step on the time-scale plane directly. And the accurate AM frequency of the specific fault is then identified by spectral analysis on the computed IA. The TSM signature concerns both nonstationarity and nonlinearity of the measured signal, and has excellent effect of de-noising, which ensures the good performance for the proposed fault frequency identification method.
The remainder of this paper is organized as follows. Section 2 presents details on how to produce the TSM signature, where a selection method of scale range is also proposed. Section 3 further proposes a novel feature extraction method, called TSM ridge analysis, as well as a new fault diagnosis scheme. In Section 4, practical applications to gearbox fault diagnosis and bearing defect identification are conducted, respectively, to verify the effectiveness of the proposed methods. Finally, conclusions are drawn in Section 5.
Section snippets
TSM
The CWT can characterize a non-stationary signal at different localization levels simultaneously in time and scale. The variation of the amplitudes of wavelet coefficients on the time-scale plane is called TSD. When a fault happens in a rotating machine, the TSD of observed signal can represent the fault features at specific scales periodically along the time axis, and thus reflect abundant non-stationary information over the whole spectrum. The TSD in the same conditions will indicate a
TSM ridge analysis
For a physical interpretation, the TSM represents the underlying energy distribution of the signal in the time-scale domain. The energy mainly concentrates around a curve, which can be called as the TSM ridge. The fault component of the observed signal possesses most of the energy in the TSM. Therefore, the analysis of the TSM ridge which lies on the TSM signature is of great significance. Since the ridge of TSM lies on the time-scale plane and the scale axis can be converted into frequency
Applications in rotating machine fault diagnosis
In this section, three sets of defective signals of rotating machine are analyzed for fault feature extraction and identification by the proposed TSM signature and TSM ridge analysis. The first is gearbox data with severe wearing fault. The other two sets are ball bearing and train bearing data with defects at the outer raceway, inner raceway, and rolling element. To compare the identification effect of the fault-induced frequency, these data are also addressed by the EMD-based and the
Conclusions
This paper presents a new time-scale signature, called the TSM, by combining the CWT and the non-linear manifold learning, for representing intrinsic machinery fault pattern, and explores the TSM ridge to identify the fault characteristic frequency. The TSM signature concerns the nonstationarity of the faulty signal, and reveals the non-linear structure related to the fault. Hence, it shows the merits of high SNR and good time-scale resolution for representation of fault signature in a running
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant 51005221, the Research Fund for the Doctoral Program of Higher Education of China under Grant 20103402120017, the National Natural Science Foundation of China under Grant 51075379, and the Startup Funding for New Faculty of the University of Science and Technology of China. The authors would like to thank the CWRU for supplying the ball bearing experimental data. The anonymous reviewers are sincerely
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