Journal of Sensors

Volume 2019, Article ID 6207847, 11 pages

https://doi.org/10.1155/2019/6207847

## A Fault Diagnosis Method of Train Wheelset Rolling Bearing Combined with Improved LMD and FK

Correspondence should be addressed to Yu Zhang; moc.361@reuy.gnahz

Received 9 May 2019; Revised 1 August 2019; Accepted 27 August 2019; Published 4 December 2019

Academic Editor: Stelios M. Potirakis

Copyright © 2019 Yu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Trackside acoustic signals contain intense noise and nonstationary features even after Doppler distortion correction. Information on bearing defects in these signals is either weak or heavily attenuated. Thus, an improved compound interpolation envelope local mean decomposition (ICIE LMD) method combined with a fast kurtogram (FK) is proposed for wheelset bearings. In this methodology, cubic Hermite interpolation and cubic spline interpolation are employed to find the envelope of the extremal points in the ICIE LMD algorithm to improve accuracy and decrease the computing time of the decomposed signal component. An FK is sensitive to the impact signal and extracts the fault impact features efficiently. In the application, the proposed method uses ICIE LMD to decompose the multicomponent signal into several specific single product function (PF) components. The kurtosis index of the PF is calculated to select the component which contains the most fault information. Then, the selected component of PF is filtered by FK. Finally, the squared envelope spectrum is used to obtain the fault frequency and identify the fault location. The advantages of the ICIE LMD method are verified by simulation analysis. In the application, the results show that the proposed method efficiently extracts the fault features and enhances the target characteristics of the sound signals from a trackside microphone array. Furthermore, the influence of rotating frequency on locating the fault is reduced.

#### 1. Introduction

The wheelset bearing of a high-speed train is an indispensable component that is prone to damage when the train is running. Bearing damages and defects directly affect the stable operation of equipment [1]. The defects, such as pitting corrosion and cracks, happen on the contact surface of the rolling bearing quickly, when the bearing is under the alternating contact force for a long time, especially when a train is running at high speed and with the heavy loads [2]. Traditional diagnosis methods for high-speed train rolling bearings are mostly done by the vibration signal. Because of the application of the trackside microphone array system in railway inspection, it is important to analyse the acoustic signal of the rolling bearing obtained from the microphone. The difference between the two types of signal is that the vibration signal is collected directly on the surface, whereas the acoustic signal is picked up through the propagation in the air. The acoustic signal becomes weaker, and much more noise and a complicated reflection are introduced, heavily distorting the original signal. Furthermore, collection diversity influences the efficiency and accuracy of the current fault diagnosis method.

The key to fault diagnosis is mainly extracting the fault feature from the rolling bearing signal [1]. When a fault happens, the collected signal is a multicomponent modulation signal, whose characteristic is nonstationary and nonlinear. Time-frequency analysis is widely used for fault diagnosis, such as short-time Fourier transformation (STFT), Wigner-Ville distribution, and wavelet transform [3]. However, the methods mentioned produce an individual decomposed result when processing a signal, but the limitation is that they are not adaptive [4]. For instance, wavelet analysis cannot denoise a weak signal because of the selection problem of the wavelet basis function and decomposition level [5, 6]. Empirical mode decomposition (EMD) has the problem of mode mixing. When the signal is decomposed into a sequence of intrinsic mode functions (IMFs) by EMD, the characteristic time scales of IMFs vary [7].

Local mean decomposition (LMD) is a new signal-processing method developed by EMD and proposed by Smith [8]. LMD decomposes the nonstationary signal into the product function (PF) of a purely frequency-modulated signal and envelope signal component [9]. It can be decomposed adaptively according to the practical scale characteristics of the signal and can solve the mode-mixing problem caused by EMD [10]. However, the end effect and mode mixing still exist in LMD decomposition. Xu et al. [11] introduced an energy-matching extension method to solve the end effects, verified by the simulated signal. To weaken the influence of end effects, Du et al. [12] considered the signal a discrete difference, determining the value of extreme points of continuation according to the specific situation. The result of the new method was adapted to the signal of the rolling bearing with the outer raceway and inner raceway improved by mirror extension. Ensemble LMD (ELMD) was proposed by Yang et al. [13], which adds the Gaussian white noise into the original signal and changes the extreme point distribution of the signal. According to the decomposition characteristic of ELMD, a method of K-L divergence used adaptively in selecting the principal PFs was proposed by He and Zhou [14].

The accuracy of PF components is affected by the envelope function of LMD. The moving averaging method applied in the original LMD produces a phase error of functions under the running of the algorithm [15]. Hu et al. [16] developed a method to obtain the envelope estimation function by applying cubic spline interpolation to calculate the envelopes of local extreme points. This method improves computation time, but undershoot and overshoot problems of the envelope are observed for signals with strong nonstationary features [17]. Spline-based LMD, combined with the second-generation wavelet, is suitable for extracting the fault feature of the weak fault signals [18]. In a previous work [19, 20], the moving average was replaced by monotonic piecewise cubic Hermite interpolation (MPCHI) in the LMD algorithm, and this increased the accuracy of the PF components that contained the feature of the nonstationary signal. MPCHI can avoid the undershoot and overshoot problems of the envelope with a nonstationary signal. However, the acoustic signal and vibration signal mix several nonstationary and stationary parts. Hence, Zhao et al. [21] proposed a method combined with cubic spline interpolation (CSI) and MPCHI to obtain the envelope of extreme points in the LMD method. The nonstationary coefficient was defined to divide the envelope of the signal into the CSI and MPCHI parts.

The fast kurtogram (FK) was developed based on spectra kurtosis (SK), which is mainly used to calculate the kurtosis value. The kurtosis value is susceptible to transient signals, which reflect the numbers of nonstationary components included in each frequency curve [22]. FK is used to optimize the centre frequency and bandwidth of bandpass filters and then extract the pulses. Barszcz and Randall [23] explored some methods usually applied to fault detection and online diagnosis. The result shows that only the SK method can recognise catastrophic gear failure. Zhang and Randall [24] combined genetic algorithms and FK for rolling component bearings. The experiment illustrated the effectiveness of the approach. It was proved to provide better results than resonance demodulation. The FK gives simple processing results very efficiently. When applied individually, the FK can extract the pulse but cannot recognise the fault location because of the rotating frequency influence.

Concerning the problems mentioned, the improved compound interpolation envelope (ICIE) LMD combined with FK is presented to extract the fault feature of the rail-side acoustic bearing signal. First, the original signal is decomposed into several single components by ICIE LMD. Second, the kurtosis value is calculated for each element. Because kurtosis is sensitive to a shock signal, the component with the maximum value of kurtosis is selected for FK analysis, and the square envelope spectrum is used to extract fault feature information. The average peak signal-to-noise ratio (PSNR) of the method is used to show the efficiency of the proposed method for fault diagnosis. The results show that this method can effectively extract and enhance the fault characteristics of the trackside acoustic rolling bearing and weaken the influence of rotating frequency.

The theories of CSI LMD, ICIE LMD, and FK are briefly introduced in Section 2. In Section 3, the simulation analysis of ICIE LMD with artificial data is shown. In Section 4, the proposed method is applied to the fault diagnosis of the real trackside acoustic bearing signal. The conclusions are outlined in Section 5.

#### 2. Improved LMD Method

##### 2.1. Principle of CSI LMD

LMD adaptively decomposes the signal into a series of PF components, which are the product of a purely frequency-modulated signal and an envelope signal. The frequencies of the decomposed PF components are arranged automatically from high to low. According to the CSI LMD algorithm, the upper and lower extreme envelopes are derived by CSI for two functions, replacing the moving-averaging method in the classical one [25]. The algorithm is as follows [25]:
Step 1.The local maximum and minimum points of the given signal are acquired, and then the upper envelope and the lower envelope of extrema are obtained by CSIStep 2.The local mean value and the envelope function are derived by the upper envelope and the lower envelope as
Step 3.The local mean value is separated from the primitive data Then is divided by , illustrated as
The above steps are repeated, and the envelope function can be acquired. Ideally, if is a purely frequency-modulated signal, which means , the procedure ends. If not, is regarded as primitive data, and the above step is iterated again until satisfying the above demand. However, in practice, the envelope function cannot be exactly 1. The threshold value *Δ* is set. When , iteration endsStep 4.The corresponding envelope is calculated as
The first product function can be obtained by
Thus, is given by subtracting from the original signal . is regarded as an initiative signal to do all steps until it is monotonic. After that, is represented as

##### 2.2. Improved Compound Interpolation Envelope Algorithm

Because of the envelope problem of undershoot and overshoot in the CSI method, the compound interpolation envelope LMD (CIE LMD) was proposed by Zhao et al. [21]. It defined the nonstationary coefficient to represent the state of the signal. The threshold of the nonstationary coefficient is chosen to divide the signal into a stationary section and nonstationary section. The envelope is made compound by CSI for the stationary part and MPCHI for the nonstationary part of the signal. However, compared with CSI LMD, the way to calculate the nonstationary coefficient and envelope increases the computing time in CIE LMD.

Therefore, the ICIE LMD method applies the CHI method, replacing the MPCHI method, to simplify the algorithm and reduce the central processing unit (CPU) time. The definition of the CHI method is given as follows.

For the interval [a, b], the node series is and the function value is . When , is defined as , and is defined as . The interpolation function of CHI is

For the same series , the interpolation function of MPCHI is described as Equation (8) [21].

The parameters in the formula are defined by

The first derivative is where and . If the data are monotonic, i.e., or ,

The MPCHI method needs to make a judgment on the data for their monotonicity before processing. Moreover, it has a different way to calculate the derivative values compared with CHI. The factors cause CPU time to increase.

Furthermore, the threshold of the nonstationary coefficient is calculated by the arithmetic mean in Equation (12) in ICIE LMD to adapt the different types of signal and obtain better accuracy.

Then, the steps of the ICIE LMD algorithm [21] are as follows: Step 1.The local extrema series of the given signal is calculated, and the maximum extrema series and minimum extrema series are dealt with separatelyStep 2.The slope of one of the extrema series is calculated; after that, the nonstationary coefficient is calculated by Equation (13) Step 3.The threshold value of the nonstationary coefficient is obtained by Equation (12). The value of nonstationary points is larger than . Their position is recorded as Step 4.The point is and its previous one is , and the following one is , all as interpolation points for CHI; the local CHI interval is . If the number of extrema points between two nonstationary points and is less than five, the two CHI intervals are connected as ; if the number of extrema points between nonstationary point and the left or right extrema series is less than three, the initial local CHI interval is and the end interval is Step 5.For the rest of the stationary points, the CSI envelope is created in the same way as in Step 4Step 6.If all CHI intervals are empty, the CSI method creates the whole extreme series. Similarly, if all CSI intervals are empty, the envelope is created by the CHI methodStep 7.To compound the two types of envelope, the connecting endpoints of the local CHI interval are assigned to CSIStep 8.The above steps are repeated to obtain the envelopes of other extrema series

This method is applied to replace the first step of the CSI LMD method presented in Section 2.1, and keeping the remaining procedures, the ICIE LMD is illustrated.

##### 2.3. Fast Kurtogram

In rolling bearing faults, the existence of transient vibration signals is highly correlated with cracks and clearances. SK is a useful transient signal detection technology. Antoni [26] established the spectral kurtosis theory in 2006, defining the spectral kurtosis by STFT and developed the fast kurtogram algorithm.

The spectral form of the World-Cramer decomposition is defined in the nonstationary state.

The nonstationary signal and the stationary noise are mixed, and their SK is calculated as where is an orthonormal spectral increment and is a complex envelope of at frequency and time note is the noise-to-signal ratio of the mixed signal. When the value of is close to zero, no noise exists here. When is close to the bandwidth of the fault characteristic signal, the function of the frequency and window length reaches the maximum.

Therefore, the centre frequency and bandwidth of the bandpass filter can be optimized by the FK algorithm, and the narrowband impact signal can be extracted under a condition of substantial noise. The flowchart of the proposed method applied in fault detection for rolling bearings is shown in Figure 1.