The rapid development of complex systems such as power plants, high-speed transportation vehicles, and high-precision machining centers has been emphasizing the need for condition monitoring and diagnosis so as to maximize operational availability and safety. Therefore, research on prognostics and health management (PHM) has attracted the interest of industry and academia due to its great potential to address these needs. In the process of PHM implementation, data preprocessing and feature extraction are the fundamental modules, since their outputs are used for system health assessment and prediction. However, the complicated structures and working conditions of complex systems may result in multiple faults during their operation that produce multi-frequency signals and lead to a challenging problem called multi-fault diagnosis. In these situations, frequency aliasing arises, and fault-related components may be too close in the frequency domain to be effectively identified for further feature extraction and diagnosis.
The identification of characteristic components is fundamental and important for complex system feature extraction and health assessment. Along with the development of signal processing, more and more techniques have been introduced to diagnose faults in machinery. The methods used for characteristic component identification or fault character extraction usually can be classified into the frequency domain and time domain methods. Time domain methods provide high frequency selectivity and high estimation accuracy, but require computation-intensive algorithms to determine the optimal model order. Frequency domain methods use the discrete Fourier transform (DFT) to calculate the spectrum and estimate the frequency parameters of a signal. On account of some inherent drawbacks, the traditional DFT-based approaches have some restrictions in practice. For example, it is hard to obtain accurate frequency, amplitude, and phase information about synchronous vibration and its harmonic or subharmonic components because of the leakage and the picket-fence effect of the DFT spectrum.
In order to enhance the efficiency and accuracy of fault diagnosis, it is crucial to improve the estimation accuracy of amplitude, frequency, and phase of signal for feature extraction in the frequency domain. The method used to deal with this problem is called "windowing."
One frequency domain method often used for estimating multi-frequency signal parameters under noncoherent sampling is the interpolated DFT (IpDFT) method, which provides very accurate parameter estimates. For example, Ramos and Serra from the Technical University of Lisbon compared the frequency algorithms of IpDFT, Chirp-Z transform, Hilbert transform, STFT, CWT, MUSIC, Sine-fit, and Kalman filtering. They determined that the IpDFT algorithm is the most precise, accurate algorithm as well as the fastest. Rife and Vincent proposed a specific approach in Bell Syst. Tech. Journal called the interpolated fast Fourier transform (IFFT), to dramatically improve the accuracy of the FFT spectrum. Moreover, Jain et al. proposed an approximate interpolation algorithm in IEEE Trans. Instrum. Meas. Vol. 28, which is used to obtain accurate amplitude, phase, and frequency information when a rectangular window is employed. Shi et al. from the University of Manchester, proposed the general IFFT for diagnosing faults in large rotating machinery, but the algorithm is very complicated.
The performance of the IpDFT method depends on the window used, and it should be noted that the formulas for estimating the parameters of a multi-frequency signal are very complicated foremost windows. Among all these windows, the maximum sidelobe decay windows are frequently employed in the IpDFT method. The IpDFT method with maximum sidelobe decay windows leads to very accurate estimates, since the parameters of a multi-frequency signal can be estimated by analytical formulas. Belega and Dallet from the University of Timisoara and the University of Bordeaux, proposed accurate and simple formulas for estimating the variances of the estimators of the parameters of a multi-frequency signal obtained by the IpDFT method with maximum sidelobe decay windows.
This study was conducted to investigate the potential of the IpDFT with maximum sidelobe decay windows in machinery (e.g., gearbox, bearing) feature extraction and condition monitoring. An IpDFT-based method combining the idea of local frequency band zooming-in (i.e., the zoom IpDFT) is proposed in this research to further improve the identification capability of multiple adjacent characteristic components in the frequency domain, which is a challenging issue for complex system condition monitoring and PHM.
The real motor bearing data picked up with a sampling frequency of 12k Hz by an accelerometer placed at the drive end of the motor housing were used to validate the proposed method. Three kinds of bearing conditions were considered in this case study, namely the normal condition, the inner race fault condition, and the outer race fault condition. The accelerometers under the normal conditions and inner race fault conditions were placed at the 12 o'clock position, while under the outer race fault conditions they were placed at the 6 o'clock position. The test rig is shown below.
Single point faults were introduced to normal bearings using electro-discharge machining with a fault diameter of 0.007 inches and a fault depth of 0.011 inches. The shaft rotation speed varied from 1730 to 1797 rpm. There was a total of 12 datasets, including 4 normal bearings, 4 inner race fault bearings, and 4 outer race fault bearings at different rotation speeds and workloads.
The following identification methods were used in the 4 sessions:
In machinery condition monitoring, the identification of fault-related characteristic components is a crucial step to realize feature extraction for further diagnosis. In this study, the IpDFT with maximum sidelobe decay windows is investigated for its identification of characteristic components in the frequency domain.
A novel method based on the IpDFT is then proposed to combine the idea of local frequency band zooming-in, which is called the zoom IpDFT. In this process, the IpDFT with maximum sidelobe decay windows can estimate the components of a signal accurately and stably. The proposed zoom IpDFT based on multiple modulations provides better performance in signal parameter estimation with high accuracy and frequency resolution, especially in a situation of multi-fault diagnosis in which frequency aliasing exists and fault-related components may be too close in the frequency domain to be effectively identified.
To validate the proposed zoom IpDFT method, a series of experiments was conducted in this study. The zoom IpDFT method was tested using vibration data collected from a motor bearing at a rotation speed of 1797 rpm and a load of HP 0. The method identified fault-related characteristic components in the frequency spectrum. It was then used to identify the characteristic components at different loads and rotation speeds, and the results showed good potential in characteristic frequency identification. Comparison studies of the Fourier transform and the IpDFT method using bearing vibration data with inner race fault and outer race fault showed that the IpDFT method can provide distinct results in characteristic frequency identification with low frequency bias and accurate frequency amplitude estimation. Later, a mixed signal containing two adjacent fault characteristic frequencies was constructed to compare the proposed zoom IpDFT with other methods, including the FFT and the zoom FFT. The comparison results of the mixed signal using the FFT, the zoom FFT, and the zoom IpDFT indicated that the zoom IpDFT can identify the two fault characteristics with good accuracy and frequency resolution.
It should be noted that the vibration signals from rolling element bearings usually exhibit pseudo-cyclostationarity, which means that there exists stochastic variation in the spacing of the bursts generated by the local faults on rolling elements and races. This effect causes random slip during bearing operation and leads to a certain degree of variation in the frequency domain. Therefore, the proposed method in this research is most applicable to the separation of discrete frequency components, which is more popular in gear systems.
For details, please contact CityU PHM Centre > phmc@cityu.edu.hk
Source: Qiang Miao, Lin Cong and Michael Pecht, "Identification of Multiple Characteristic Components with High Accuracy and Resolution Using the Zoom Interpolated Discrete Fourier Transform", Meas. Sci. Technol. 22 (2011) 055701 (12pp); doi:10.1088/0957-0233/22/5/055701
