Multi-scale enveloping spectrogram for vibration analysis in bearing defect diagnosis
Introduction
Demand for better product quality and reliability has led to increased sensor integration in machine systems to enable more comprehensive, accurate, and timely gathering of information on their working status. Various sensors have been developed and employed over the past decades that measure vibration (acceleration), dynamic force, acoustic emission, or temperature during machine operations for condition monitoring and defect diagnosis. Since vibration signals are directly associated with the structural dynamics of the machine being monitored, vibration measurement has been widely adopted as a popular tool. Effective utilization of the vibration data, however, depends upon the effectiveness and efficiency of the signal processing technique employed to extract characteristic features (i.e. defect-induced vibration components) from the signal and assess how severe the defect in the machine system is and what needs to be done to correct the problem and ensure continuous, safe operation. This indicates that proper signal analysis is a critical prerequisite for clear identification of machine conditions, timely diagnosis of defect severity, and reliable prediction of the remaining service life. Proper signal analysis is also critical to establish the platform for automated and condition-based flexible maintenance scheduling, as opposed to the traditional, fixed-interval maintenance, to minimize machine downtime, improve productivity, while reducing maintenance cost.
A large number of applications in machine condition monitoring involve rotary machine components (e.g. bearings, spindles, and gearboxes) [1], [2], [3]. To detect structural defects that may occur in these machine components, spectral analysis of the signal's envelope has been widely employed [4], [5], [6]. This is based on the consideration that structural impacts induced by a localized defect often excite one or more resonance modes of the structure and generate impulsive vibrations in a repetitive and periodic way. Frequencies related to such resonance modes are often located in higher frequency regions than those caused by machine-borne vibrations, and are characterized by an energy concentration within a relatively narrow band centered at one of the harmonics of the resonance frequency. By utilizing the effect of mechanical amplification provided by structural resonances, defect-induced vibration features can be separated from the background noise and interference for diagnosis purpose. In Fig. 1, the procedure for such an enveloping and band-pass filtering-based spectral analysis technique is illustrated.
An inherent limitation when applying this technique is that it requires proper filtering band be chosen upfront to obtain consistent results under varying machine operating conditions, as these will cause different resonance modes to be excited. Due to this limitation, detecting machine defects at the incipient stage when defect-characteristic components are weak in amplitude and without a distinctive spectral pattern poses a challenge to the conventional enveloping spectral analysis technique. Several modified spectral techniques have been introduced to overcome the above described difficulty, such as short time Fourier transform (STFT) and repetitive Fourier transform (RFT) [7]. While these techniques are more accurate in identifying defect-related frequencies, they require a priori knowledge about the possible location of defect-related frequency lines in order to determine the size of the analysis windows. In practice, such determination is satisfied only through a trial-and-error process.
To overcome these limitations, the wavelet transform has been increasingly investigated [8], [9], [10], [11], [12]. Unlike the Fourier transform, which expresses a signal as the sum of a series of single-frequency sine and cosine functions, the wavelet transform decomposes a signal into a set of basis functions, which are obtained from a single base wavelet by scaling (dilation/contraction) and time shift (translation), to measure the “similarity” between the signal and the base wavelet. Through variations of the scales and time shifts of the wavelet function, the wavelet transform is capable of extracting signal features over the entire spectrum, without requiring the signal having a dominant frequency band. On the other hand, since it is a time-scale domain technique, wavelet transformation does not provide or make use of the frequency characteristics of the signal, which can be inherently embedded in the signal due to the periodical nature of the signal generation (e.g. balls rolling over a raceway crack periodically as the bearing rotates). Complementing the wavelet transform with frequency information related to the defect characteristic would significantly enhance the effectiveness in defect signal extraction. Based on this motivation, a multi-domain signal feature extraction technique termed multi-scale enveloping spectrogram (MuSEnS) has been developed and presented in this paper. After introducing the theoretical background in Section 2, details of the MuSEnS technique is discussed in Section 3. Subsequently, numerical simulation is performed to evaluate the proposed new technique quantitatively, where different signal processing techniques are compared with the new technique. In Section 4, experimental validation using data collected from the rolling element bearings is presented. Conclusions are drawn in Section 5.
Section snippets
Signal enveloping through Hilbert transform
Envelope extraction from a signal has been traditionally realized by rectifying and low-pass filtering the signal, which is previously band-pass filtered. On the other hand, the Hilbert transform has shown to present a good alternative to forming a signal's envelope [13]. Mathematically, the Hilbert transform of a real-valued signal x(t) is defined aswhere denotes the Hilbert transform operator. The symbol represents a real-valued signal, and can be
Formulation of multi-scale enveloping spectrogram
The MuSEnS algorithm was developed by making use of the time, scale, and frequency domain information contained in the signal in a synergistic fashion. Computationally, it first decomposes the signal (e.g. vibrations measured on a defective rolling bearing) into different wavelet scales by means of a complex-valued wavelet transform, as illustrated in Fig. 2a. The envelope signal in each scale (Fig. 2c) is then calculated from the modulus of the wavelet coefficients (Fig. 2b). Subsequently,
Experimental evaluation
To experimentally evaluate the MuSEnS algorithm, vibration signals measured on two types of bearings under different working conditions are analyzed, and the results are discussed as follows.
Conclusion
A new vibration signal analysis algorithm has been developed to extract defect-related features. This multi-domain signal processing technique combines the advantages of the wavelet transform (in flexible time–scale signal representation), Fourier-based spectral analysis (indicating the intensity and location of defect-induced characteristic frequency lines), and color mapping into one integrated platform, which enables more effective bearing defect diagnosis. The effectiveness of the developed
Acknowledgments
The authors gratefully acknowledge funding provided to this research by the National Science Foundation under award DMI-0218161. Experimental support from the SKF and Timken companies is acknowledged.
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