A novel signal compression method based on optimal ensemble empirical mode decomposition for bearing vibration signals
Introduction
In industry, remote condition monitoring systems are designed to collect data for remotely assessing the health condition of important machine elements. For example, rolling bearings are the most important elements in the vast majority of rotating machines. Serious bearing failure may cause downtime costs or significant damage to other parts of the machine, and even catastrophic failure [1]. Hence, it is vital to transmit vibration signals generated from the bearings in a monitored machine to the maintenance center for determining the health conditions of bearings.
Unfortunately, the performance of remote monitoring is often affected by the problem of needing to transmit large amounts of data collected by sensors. To ensure diagnostic accuracy of rotating machines, sufficient vibration data are needed. A data acquisition system samples data through many channels simultaneously at a high sampling speed which is usually set at fifty thousand samples per second or higher. Therefore, the amount of data required for fault diagnosis is often massive [2]. However, the data transmission from a local source or a monitored machine to a remotely located maintenance center over wireless channels faces bottlenecks, such as limited bandwidth and long transmission time. To minimize the storage and transmission load, it is necessary to compress the collected raw data to an acceptable size prior to wireless transmission. The compression of data can be achieved by removing redundant and irrelevant information from the raw vibration data and compressing the data that can fit into the limited bandwidth and enable fast transmission. When the maintenance center receives the compressed data, it must ensure that the received data can be reconstructed back to its temporal waveform without losing any information that is vital for accurate fault diagnosis.
The existing signal compression methods can be categorized into three types: direct data compression methods, parameter extraction methods and transformation methods. In direct compression methods, the signal is directly handled to provide the compression. Coding by time domain methods is based on the idea of extracting a subset of significant samples to represent the original signal [3], [4]. Parameter extraction methods use a pre-processor to extract parameters or features of the signal and perform compression on them; for example, the compression method based on linear predictions or neural networks (e.g., [5], [6]). Compression methods based on transformations (e.g., S transform [7], fractional Fourier transform [8], discrete cosine transform [9], and wavelet transform [10]) transform the signal in the time domain to another domain and then compress a small portion of the transform coefficients. Among the transform methods, wavelet transform has shown promising performance due to its good localization properties [2], [11].
Various wavelet-based compression methods for one-dimensional signals have been proposed to compress the electrocardiograph signal (e.g., [12], [13]) and speech signal [14], whereas only a few results [10], [15], [16], [17] were the compression of vibration signals using wavelet transform. One of major problems with wavelet transform is their non-adaptive basis because the selection process of the best basis function is dominated by the signal components that are relatively large in a frequency band [18]. No general guidelines have been proposed for properly selecting the wavelet basis function [19]. Meanwhile, little attention has been paid to inherent deficiencies of the wavelet transform, such as border distortion, energy leakage, etc. [20], [21].
An adaptive signal processing method, empirical mode decomposition (EMD) method [22], [23] has recently been paid attention. This method represents nonlinear and non-stationary signals as sums of simpler components with amplitude and frequency modulated parameters [24]. It has no limitations in terms of basis function selection, energy leakage, parameter selection of model, and so on. It has been shown to be quite versatile in a broad range of applications for extracting signals from data generated in noisy nonlinear and non-stationary processes [25], e.g., [21], [26], [27]. The ensemble empirical mode decomposition (EEMD) [28] has been recently developed from the EMD method and can improve its scale separation.
In relation to vibration signals collected from faulty bearings, the EEMD method can be employed to extract impulsive shocks, which are generated when a faulty rolling ball strikes either the inner race or outer race, or when balls strike a faulty outer or inner race, or even both races. This paper proposed a novel signal compression method based on the optimal EEMD method for bearing vibration signals. The method involves two steps. First, the EEMD method with parameter optimization is used to decompose a vibration signal collected from a faulty bearing, so that the signal component related to the defect characteristics can be separated from background noise and the other irrelevant signal components. The designed parameter optimization automatically selects appropriate EEMD parameters for the vibration signal to be analyzed. Second, a subset of significant samples is selected from this signal component for compression.
The remainder of the paper is organized as follows. Section 2 provides a brief introduction to the EEMD method and a review of published methods for determining the EEMD parameters. Section 3 first gives an empirical strategy of the EEMD parameters and then presents an optimization method for the EEMD parameters. Section 4 proposes a signal compression method for the compression of bearing signals and compares it with the popular wavelet compression method. Fault diagnosis is conducted to verify whether the proposed compression results in the loss of defect characteristics in bearing signals. Section 5 applies the proposed methods to a vibration signal collected from a real traction motor. Finally, conclusions are drawn in Section 6.
Section snippets
Brief introduction of EEMD
The EEMD method [28] was developed from the EMD method [22], [25]. It belongs to noise-assisted signal analysis methods and has been proven with better scale separation ability than the normal EMD method. The procedure of the EEMD method can be briefly summarized as follows:
Step 1:Add white noise with a predefined noise amplitude to the signal to be analyzed.
Step 2:Use the EMD method to decompose the newly generated signal.
Step 3:Repeat the above signal decomposition with different white noise,
Observations on parameter setting
Wu and Huang [28] described the effect of the added white noise and these two parameters satisfy the following equation thatwhere e represents the standard deviation of error between the original signal and the corresponding IMF(s). The empirical setting is as follows: the amplitude of the added white noise is approximately 0.2 of a standard deviation of the original signal and the value of the ensemble is a few hundreds. This is not always usable for signal processing in
Vibration signal compression
After applying the optimal EEMD method, the vibration signals collected from faulty bearings were decomposed into various signal components and the impulsive shocks in the vibration signals were distributed in the selected IMFs. In this section, the compression of bearing signals will be performed on the selected IMFs. Its compression performances are evaluated and compared with the wavelet compression method.
Application in a traction motor
When a train company is performing tests on a traction motor, the motor will be removed from the train and re-installed back to the train after the completion of test. It is to ensure that the motor can be tested accurately without the influence caused by the train running on a rail. Once the purpose methods have been tested successfully, then the motor can be re-tested again when the train is running on a rail. A vibration signal was collected from such a traction motor to validate the
Conclusions
This paper presents a new signal compression method based on the optimal EEMD method for bearing vibration signals. An optimization method was designed for automatically selecting appropriate EEMD parameters for the vibration signal to be analyzed, so that the significant feature signal of the faulty bearing can be extracted from the original vibration signal and separated from background noise and the other signal components that are low-correlated or irrelevant to bearing faults. After
Acknowledgements
We acknowledge all the reviewers and the editor for their valuable comments. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 122011) and a grant from City University of Hong Kong (Project No. 7008187).
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