Journal of Sensors

Volume 2019, Article ID 8498496, 12 pages

https://doi.org/10.1155/2019/8498496

## A Hybrid Time-Frequency Analysis Method for Railway Rolling-Element Bearing Fault Diagnosis

State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

Correspondence should be addressed to Dong Zou; moc.361@nh_gnodz

Received 27 June 2018; Revised 25 September 2018; Accepted 18 October 2018; Published 10 January 2019

Guest Editor: Giuseppe Campobello

Copyright © 2019 Yao Cheng 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

The health condition of rolling-element bearings is important for machine performance and operating safety. Due to external interferences, the impulse-related fault information is always buried in the raw vibration signal. To solve this problem, a hybrid time-frequency analysis method combining ensemble local mean decomposition (ELMD) and the Teager-Kaiser energy operator (TKEO) is proposed for the fault diagnosis of high-speed train bearings. The ELMD method is a significant improvement over local mean decomposition (LMD) for addressing the mode-mixing problem. The TKEO method is effective for separating amplitude-modulated (AM) and frequency-modulated (FM) signals from a raw signal. But it is only valid for monocomponent AM-FM signals. The proposed time-frequency method integrates the advantages of ELMD and TKEO to detect localized defects in rolling-element bearings. First, a raw signal is decomposed into an ensemble of PFs and a residual component using ELMD. A novel sensitive parameter (SP) is introduced to select the sensitive PF that contains the most fault-related information. Subsequently, the TKEO is applied to extract both the amplitude and frequency modulations from the selected PF. The experimental results of rolling element and outer race fault signals confirmed that the proposed method could effectively recover fault information from raw signals contaminated by strong noise and other interferences.

#### 1. Introduction

Rolling-element bearing is a critical component of rotating machinery. The malfunction of a rolling-element bearing can cause a decrease in performance or even catastrophic failure with huge economic losses. To monitor the health condition and detect localized defects in a rolling-element bearing, many signal-processing techniques have been proposed and developed in recent years. As one of the most widely-used methods for vibration signal analysis, time-frequency methods, including wavelet transform [1, 2], time-frequency distribution [3, 4], time series model [5, 6], matching pursuit [7, 8], and empirical mode decomposition (EMD) [9], have been explored as powerful tools for fault detection and diagnosis of rolling-element bearings.

Local mean decomposition (LMD), originally proposed by Smith [10] in 2005, is a nonparametric, data-driven time-frequency decomposition method. It adaptively decomposes any complicated multicomponent signal into a series of product functions (PFs), each of which is a product of an envelope signal and a purely frequency-modulated (FM) signal. In addition, the instantaneous amplitude and frequency of each PF can be calculated directly according to the envelope and purely FM signals, respectively. Based on its inherent advantages, LMD is effective for analysing any complicated signal with time-varying frequency, phase, and energy. Most importantly, compared with EMD, the results of LMD are physically plausible, making the conclusions drawn from LMD relevant for various applications. Because of its simple implementation and adequate ability to reveal a signal’s nonstationary and nonlinearity information, LMD is widely used as a time-frequency analysis tool for fault diagnosis in rotating machinery [11–15]. However, the mode-mixing phenomenon has a significant influence on the results. It causes LMD to produce different scale oscillations in a single PF or similar scale oscillations in multiple PFs, resulting in some PFs with no physical meaning in the decomposition results. To overcome this drawback of LMD, Yang et al. [16] proposed a noise-assisted time-frequency analysis method called ensemble LMD (ELMD) in 2005. With ELMD, an ensemble of white noise is added to the original signal, and then the LMD method is used to decompose each of these signals into a series of separate PFs. The final PFs are calculated by averaging the corresponding PFs derived by LMD. The ELMD method can adaptively filter local oscillations into appropriate PFs through the uniform filtering characteristics of white noise, reducing the mode-mixing phenomenon and achieving better decomposition performance compared with LMD. Owing to this significant improvement, ELMD has a diverse range of applications in rotating machinery such as bearing [17, 18] and gear fault diagnoses [19]. However, after performing ELMD on a vibration signal, the added white noise in the raw signal pollutes the PFs and residual signal according to the filter bank structure of LMD. Thus, further procedure is required to precisely and effectively detect the fault characteristic information of rolling-element bearings.

The Teager-Kaiser energy operator (TKEO) was originally proposed by Kaiser in 1990 [20] to measure the energy of a mechanical process, based entirely on the local differential operation without involving any transform. It was designed to extract the amplitude-modulated (AM) and frequency-modulated (FM) signals from a monocomponent AM-FM signal. With its localization property and low computational complexity, the TKEO method has been widely used in machinery fault diagnosis. Liang and Bozchalooi [21] applied the TKEO to extract both the amplitude and frequency modulations of the vibration signals measured from mechanical systems and validated its effectiveness using both simulated and experimental data. Tran et al. [22] proposed a new approach to valve fault diagnosis of reciprocating compressor using three widely used signals involving vibration, pressure, and current of induction motor using TKEO and deep belief networks. Studies on the use of the TKEO technique for signal and image analysis are reviewed herein [23]. It should be noted that TKEO is only valid for monocomponent AM-FM signals. Thus, TKEO always fails to modulate the fault-related information when the analysed signal contains multiple signal components showing modulation phenomenon.

In this paper, a novel hybrid time-frequency analysis method based on ELMD and TKEO is proposed for fault diagnosis in rolling-element bearings. It integrates the merits of ELMD and TKEO to detect localized defects in rolling-element bearings. First, the ELMD method is applied to decompose a multicomponent raw signal measured from faulty rolling-element bearings into a series of PFs, where each PF was a monocomponent AM-FM signal, namely, a product of an envelope signal and a purely FM signal. Second, a sensitive parameter (SP) based on correlated kurtosis (SK) and Pearson’s correlation coefficient (PCC) is employed to select the PF component that contains the most characteristic of the fault information. Finally, the TKEO is applied to extract both the amplitude and frequency modulations from the selected PF. Furthermore, the spectrum analysis is used to explore the fault information according to the appearance of the fault characteristic frequencies. To highlight the superiority of the proposed method, some comparisons with two popular signal processing methods including variational mode decomposition [24] and minimum entropy deconvolution (MED) [25, 26] were conducted in the analysis of experimental fault signals.

The rest of this paper is organized as follows. Section 2 briefly introduces the ELMD and TKEO techniques. Section 3 details the proposed hybrid time-frequency analysis method. Section 4 describes the application of the proposed technique to fault diagnosis in rolling elements. Furthermore, comparisons with VMD and MED are conducted in this section. Concluding remarks are presented in Section 5. The introduction should be succinct, with no subheadings. Limited figures may be included only if they are truly introductory and contain no new results.

#### 2. Background Theories

##### 2.1. The Theory of ELMD

###### 2.1.1. LMD

LMD is an adaptive, nonparametric time-frequency analysis method pioneered by Smith [10] in 2005. This method decomposes a raw signal into a series of PFs using the local oscillations of the signal itself. Meanwhile, the instantaneous amplitude and frequency of each PF can be estimated from the corresponding amplitude envelope and FM signals, respectively. The LMD procedure is summarized briefly as follows [10].

*Step 1. *Find the local extreme points of the targeted signal , where is the number of extreme points. Then, calculate the local mean value and local envelope magnitude of two successive extreme points as

*Step 2. *Use the moving average algorithm to smooth the local mean values and local amplitudes, and obtain a varying continuous local mean function and a varying continuous local amplitude function , respectively.

*Step 3. *Subtract the local mean function from the original signal and obtain
where is the residual signal. Then, is divided by the amplitude function , resulting in

*Step 4. *Set as the target signal and repeat steps (1–3) until a purely FM signal is obtained. This is expressed as
where

*Step 5. *The envelope signal is calculated as
and the first PF is given as
The corresponding instantaneous phase and instantaneous frequency are calculated as

*Step 6. *Subtract the derived from the original signal , obtaining the signal . Then, regard set as the new target signal and repeat the steps (1–5) until is a constant or contains no oscillations:
Finally, the original signal can be reconstructed as

###### 2.1.2. ELMD

LMD is essentially a filter bank with a self-adaptive bandwidth and centre frequency; however, it is susceptible to mode mixing. The results of LMD often contain pseudo-PFs with no physical meaning, which confuse researchers and engineers in a wide variety of fields. To improve LMD, ELMD was proposed by Yang et al. [16] to mitigate the mode-mixing problem by adding white noise to the original signal. The final ELMD PFs are calculated by taking the ensemble means of the corresponding PFs decomposed from the original signal plus the Gaussian white noise in each trial. A flowchart of the ELMD algorithm is illustrated in Figure 1:

*Step 1. *For any trial index , add the white noise to the original signal to generate the polluted signal :
where denotes the white noise with zero mean and unit variance, is the amplitude of the added white noise, and is the trial number.

*Step 2. *Decompose the polluted signal using the LMD algorithm:
where is the th PF of the th trial, denotes the residual of the th trial, and is the number of PFs.

*Step 3. *Calculate the ensemble means of the corresponding decomposed PFs:
where is the th PF for .