Shock and Vibration

Volume 2016, Article ID 2971749, 11 pages

http://dx.doi.org/10.1155/2016/2971749

## A Two-Stage Compression Method for the Fault Detection of Roller Bearings

School of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China

Received 22 January 2016; Revised 10 April 2016; Accepted 8 May 2016

Academic Editor: Daniel M. Sotelo

Copyright © 2016 Huaqing Wang 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

Data measurement of roller bearings condition monitoring is carried out based on the Shannon sampling theorem, resulting in massive amounts of redundant information, which will lead to a big-data problem increasing the difficulty of roller bearing fault diagnosis. To overcome the aforementioned shortcoming, a two-stage compressed fault detection strategy is proposed in this study. First, a sliding window is utilized to divide the original signals into several segments and a selected symptom parameter is employed to represent each segment, through which a symptom parameter wave can be obtained and the raw vibration signals are compressed to a certain level with the faulty information remaining. Second, a fault detection scheme based on the compressed sensing is applied to extract the fault features, which can compress the symptom parameter wave thoroughly with a random matrix called the measurement matrix. The experimental results validate the effectiveness of the proposed method and the comparison of the three selected symptom parameters is also presented in this paper.

#### 1. Introduction

Rotating machinery is widely applied in industrial fields, such as petrochemical industry, metallurgy industry, and power industry [1, 2]. Roller bearing, whose failure might result in the breakdown of the whole mechanical system, is considered as an integral component of rotating machinery [3, 4]. Therefore, it is essential to monitor the operating condition of the roller bearings, aiming at preventing the occurrence of the accidents.

Since much fault information is carried by the vibration signals, vibration-based diagnostic techniques have become the most commonly used and effective method for the fault diagnosis of roller bearings [5–7]. It is well known that the vibration-based fault diagnosis of roller bearings can be broadly classified into three categories, namely, time-domain analysis, frequency-domain analysis, and time-frequency analysis [8–10].

In the case of time-domain analysis, the characteristic statistical factors in time domain, including mean, peak, root mean square, skewness, can be viewed as descriptors to assess the performance of roller bearings [11–13]. Wang et al. [14] proposed a comprehensive analysis based on time-domain and frequency-domain statistical factors in order to evaluate the performance degradation degree of roller bearings. Niu et al. [15] presented some new statistical moments for the early detection of bearing failure. Heng and Nor [16] investigated a statistical method to detect the presence of defects in a roller bearing. Although the symptom parameters are easily performed to evaluate the condition of roller bearings, the successful applications are limited owing to the weak anti-interference performance of these parameters.

Compared to time-domain analysis, frequency-domain analysis has an advantage in highlighting the certain frequency components of interest by transforming the time-domain wave into frequency spectrum. The traditional method in frequency-domain is fast Fourier transform (FFT). Due to the modulation phenomenon of faulty vibration signals, envelope demodulation should be carried out before performing FFT, which is called envelope analysis. Guo et al. [17] applied envelope analysis with independent component analysis, which can extract the impulse component corresponding to the roller bearing faults and reduce the dimension of vibration sources. Wang et al. [18] developed a fault detection enhancement method based on the peak transform and envelope analysis. Cases proved that the envelope analysis can diagnose the faults of a roller bearing successfully when it is in combination with other approaches [17–19]. However, the frequency analysis will lose its effect when the vibration signals are embedded in strong noise. Thus, the time-frequency-domain analysis was developed. Many methods that belong to time-frequency analysis, such as empirical mode decomposition (EMD) [20] and wavelet transform [21], are employed to assess the performance of roller bearings. Ma et al. [22] combined local mean decomposition and time-frequency analysis, which can improve the reliability of the fault diagnosis. Li et al. [23] proposed a novel method for fault diagnosis of roller bearings based on CEEMD. Ahn et al. [24] applied wavelet analysis to eliminate noise. Though time-frequency analysis is effective in processing the nonstationary signals induced by faulty bearings, it is usually complicated and involves large computation, which is contrary to the real-time detection.

The cited literatures demonstrated that the fault diagnosis of roller bearings is developing increasingly. However, the aforementioned bearing fault diagnosis method is achieved by sampling the vibration signals under the Shannon sampling theorem. With the constraint of Shannon sampling theorem, a large amount of redundant vibration signals will be measured, increasing the burden of roller bearings’ fault diagnosis. There is no doubt that the increasing amount of data will result in high accuracy of fault diagnosis with the efficiency decreasing. Thus, it is a really tough work to balance the accuracy and efficiency of fault diagnosis.

A newly developed theory named compressed sensing (CS) [25] brought a new insight to deal with the big-data problem, which puzzled the researchers in various fields. The core idea of the CS theory is to reconstruct the original signals from a small number of samples far below the Shannon sampling rate using sparse representation and a well-designed measurement matrix. The CS theory has been applied to numerous fields, such as image processing, medical field, and remote sensing. Khwaja and Ma [26] described two possible applications of the CS theory in synthetic aperture radar image compression. Zhu et al. [27] developed an adaptive sampling mechanism on the block-based CS, which focused on how to improve the sampling efficiency for CS-based image compression. Kim and Vu [28] applied the CS theory to magnetic resonance imaging, which can be viewed as a breakthrough technology in medical diagnosis. Ghahremani and Ghassemian [29] combined the ripplet transform and the CS theory to remote sensing image fusion. All of the aforementioned studies demonstrated the possibility of applying the CS theory to the field of fault diagnosis. However, the applications of the CS theory in fault diagnosis are relatively limited. Although Zhu et al. [30] summarized the applications in the mechanical fields, no practical applications were reported. Chen et al. [31] presented a novel adaptive dictionary based on the CS theory to extract the impulse generated by the faulty bearings. Tang et al. [32] developed a representation classification strategy for rotating machinery faults based on the CS theory. Wang et al. [33] proposed a novel decomposition for reconstruction from the limited observations polluted by noise based on the CS theory via the sparse time-frequency representation. However, the aforementioned studies were primarily focused on either the sparse representation of the vibration signals or the reconstruction of the original signals, and the amount of samples in these cases still needed to be compressed.

It is significant to ensure that the few observations contain adequate faulty information, which is an essential condition to guarantee the successful applications of the compressed sensing theory. Thus, a fault features’ reservation method called the symptom parameter wave is developed to obtain sufficient faulty information. Combined with the compressed sensing theory, a two-stage compression method is described in this work to further decrease the amount of samples for fault diagnosis of roller bearings without losing significant information, through which the fault features of roller bearings can be detected timely. Compared to the work of sparse representation and reconstruction, the samples for the fault detection using the two-stage compression method are far less. First, the large amount of vibration signals is divided into several segments by a sliding window with a given size. Then, a time-domain symptom parameter is used to represent each data segment, through which a symptom parameter wave can be obtained and the original signals can be reduced to a certain level. With the symptom parameter wave, the dimension of the analyzed signals can be shrunk and it outperforms the traditional usage of these characteristic factors by representing the whole signals with single value in the presence of noise. Second, a well-designed measurement matrix is applied to compress the symptom parameter wave. Third, a fault detection method based on the CS theory is employed to extract the fault features with limited samples. Assisted by the matching pursuit, the fault features can be detected from a small number of samples, which are far below the Shannon sampling rate. Furthermore, the detection method in the current work does not need to reconstruct the original signals completely. When the components related to the fault features are detected, the reconstruction process can be finished, which means the fault diagnosis can be completed during the reconstruction procedure.

The rest of this paper is organized as follows. Section 2 introduces the basic concept of the two-stage compression strategy, followed by the compressed fault detection strategy in Section 3. The application cases are presented in Section 4. Section 5 describes the comparing results between the selected symptom parameters. Conclusions are drawn in Section 6.

#### 2. Basic Concept of the Two-Stage Compression Strategy

##### 2.1. First Stage of Compression by the Symptom Parameter Wave

As is known to all, the fault diagnosis of roller bearings based on the time-domain symptom parameters is the simplest method in time-domain analysis. The operating status of roller bearings can be identified according to the change of the time-domain symptom parameters. Generally speaking, the symptom parameters can be classified into two categories: dimensional symptom parameters and nondimensional symptom parameters. The former, such as the peak value, the peak-to-peak value, and the root mean square value, reflect the magnitude change of a signal. The latter, such as kurtosis, crest factor, and shape factor, express the shape change of a signal.

Various symptom parameters have been utilized for fault diagnosis of roller bearings. Some of them can be calculated according to the following equations:where is the peak value of a signal, represents the average of absolute value of a signal, denotes the root mean square of a signal, expresses the peak-to-peak value of a signal, is the max value of a signal, is the minimum value of a signal, SF describes the shape factor of a signal, and indicates the kurtosis of a signal.

In the traditional sense, the operating status of roller bearing can be identified by representing the whole signals with a characteristic value. This fault diagnosis method mainly depends on the difference of the characteristic values between the normal state and faulty status. However, successful cases are limited due to the instability and insensitivity of these parameters when the target vibration signals are submerged by the noise, which means the traditional usage of these symptom parameters has a weak anti-interference ability. To strengthen the ability of antinoise, a concept of symptom parameter wave is proposed in the present study. Three time-domain symptom parameters are selected to represent the signals depending on the characteristics of the faulty vibration signals. The selected symptom parameters are , SF, and , which are more sensitive to the failures than other characteristic factors. A symptom parameter wave can be achieved through a sliding window in order to compress the raw signals and preserving the fault features of the faulty vibration signals. The flow diagram of symptom parameter wave is shown in Figure 1. The raw vibration signals are divided into several segments by a sliding window and a selected characteristic parameter is used to represent each segment, through which a symptom parameter wave can be obtained. The acquisition of the symptom parameter wave can reduce the original signals to a certain level with the fault features remaining, which is the first stage of compression in this work.