An improved local characteristic-scale decomposition to restrict end effects, mode mixing and its application to extract incipient bearing fault signal
Introduction
Bearing is an indispensable part of power machinery system in modern industry but is also the main origin of system failure. It is essential to diagnose bearing fault as soon as possible before catastrophic failure. Vibration-based techniques have been proved to be the most efficient approach for bearing fault diagnosis and thus have been widely applied and developed [1], [2], [3]. In general, the measured vibration signals from fault bearings contain signals excited by localized bearing fault (termed as bearing fault signals), interference components, and environmental noise. One of the key points of bearing fault diagnosis is the accurate extraction of bearing fault signals from noisy vibration signals. Bearing fault signals are usually non-stationary, especially under variable speed condition. Thus, signal processing methods for non-stationary signals are always a topic of great interest in the fault diagnosis field [4].
Currently, time–frequency techniques are the popular way to extract bearing fault signals due to their ability to process non-stationary signals. The wavelet transformation (WT), widely used in bearing fault diagnosis, decomposes a signal into a sum of single-scale components, by the inner product between the signal and the dilatation and translation of a wavelet basis [5], [6]. However, when used to analyze practical signals, wavelet basis functions and decomposition levels must be empirically chosen. Inner-product-based signal processing methods, including Fourier transform (FT), Short Time Fourier transform (STFT), WT, and sparse representation [7], [8], share the same idea of decomposing a signal by its inner product with prototypes in a framework. Their performance depends on the similarity of morphological features between the prototypes and the signal. Empirical mode decomposition (EMD) proposed by Huang et al. [9] provides an alternative way to decompose a signal where the higher frequency fluctuations of the signal are separated iteratively, by sifting the lower frequency components out. EMD requires no priori assumptions about the content/morphology of the signal and can adaptively decompose it into a sum of intrinsic mode functions (IMFs). Adaptive analysis for non-stationary and non-linear signals makes EMD popular in a wide range of research areas, such as automatic control [10], medicine and biology [11], finance, and economic [12] and fault diagnosis [13]. The researches on EMD mainly include the following aspects: interpolation method [14], stop criterions [15], equivalent filter [16], equivalent impulse response [17], end effects [18] and mode mixing [19].
Intrinsic time-scale decomposition (ITD) which inherits the sifting-based idea was originally proposed by Frei et al. [20]. The contribution of ITD is to provide a new definition of local means of a signal, namely the baseline signal. A combination of ITD and nearest neighbor algorithm was used to identify the fault types of the wind turbine bearing [21]. Feng et al. introduced a joint amplitude and frequency demodulation analysis method based on ITD, to address the problem of complex modulations caused by the multiple modulation sources in planetary gearbox fault diagnosis [22]. Later, Cheng et al. proposed the local characteristic-scale decomposition (LCD) as an improvement of ITD with the definition of the intrinsic scale component (ISC) [23]. The essential difference between the ITD and the LCD lies in that the LCD employs multiple sifting operations at every decomposition stage, while the ITD involves single sifting operation. As a result, the LCD provides a better equivalent filter property. Zheng et al. [24] applied LCD and Fuzzy entropy to extract bearing fault features and then used adaptive neuro-fuzzy inference systems to classify bearing faults. Liu et al. [25] proposed a rolling bearing fault diagnosis method based on LCD, Teager energy operator, and multifractal detrended fluctuation analysis. The LCD provides a good performance in fault feature extraction for bearings. However, the LCD has the limitations of end effects and mode mixing resulting from the sifting process. In this paper, we proposed an improved LCD (ILCD) aiming to restrict these two problems based on support vector regression (SVR) boundary condition processing method and complementary partial noise assisted method (CPNAM). First, the signal is extended for both the left and right ends employing SVR method. Then, pairs of ISCs (positive and negative) of white noise pre-processed by LCD are added into the extended signal at the first decomposition stage. The ensemble mean of the first ISCs of the noise-added signal decomposed by LCD is regarded as the first true ISC of the extended signal. Moreover, the residue is obtained after separating each ISC, and the obtained residue is used as input for the next stage. Finally, the extended signal is decomposed as a set of ISCs and the results are shortened to the length of the original signal.
The rest of this paper is organized as follows. The background theories of the LCD are introduced in Section 2. Section 3 analyzes the equivalent filter and equivalent impulse response of the LCD compared with the EMD and the ITD to illustrate its superior. Section 4 describes the proposed ILCD which restricts the problems of end effects and mode mixing based on SVR boundary condition processing method and CPNAM. Moreover, simulation studies are conducted to demonstrate the effectiveness of the proposed method. Section 5 presents the case studies in which the ILCD is applied to diagnose bearing faults and compared with the LCD to show its effectiveness and robustness. The main conclusions are outlined in Section 6.
Section snippets
Background theory
The ITD method proposed by Frei et al. [20] and the LCD method proposed by Cheng et al. [23] are briefly described in this section.
Performance of LCD
In this section, we investigate the decomposition performance of the LCD in aspects of equivalent filter, equivalent impulse response.
The proposed method
Algorithm 5: SVR condition processing method Step1: For a given signal , extend the signal at the right end first. construct a training set where and . Step2: Construct the SVR model based on the Eq. (15). Step3: The first outer boundary can be obtained as where . Step4: Taking as the new boundary, forecast the second outer boundary based on the same
Applications
This section provides two case studies to illustrate the applications of the ILCD to extract the incipient bearing fault signal. The comparison between the ILCD and the LCD is present.
Conclusions
In a bid to restrict the problems of end effects and mode mixing of the LCD, we propose an ILCD in this paper. Through investigating its equivalent filter and equivalent impulse response and comparison to EMD and ITD, it is proven that LCD performs better with fine filter structure and the frequency resolution of LCD is related to its sifting times. By extending the boundary condition using SVR, the proposed method resolves the problem of end effects. Furthermore, introducing the CPNAM, the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China and the Civil Aviation Administration of China jointly funded project (No. U1733107), the National Natural Science Foundation of China funded project (No. 52075080).
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