Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics

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Abstract

De-noising and extraction of the weak signature are crucial to fault prognostics in which case features are often very weak and masked by noise. The wavelet transform has been widely used in signal de-noising due to its extraordinary time-frequency representation capability. In this paper, the performance of wavelet decomposition-based de-noising and wavelet filter-based de-noising methods are compared based on signals from mechanical defects. The comparison result reveals that wavelet filter is more suitable and reliable to detect a weak signature of mechanical impulse-like defect signals, whereas the wavelet decomposition de-noising method can achieve satisfactory results on smooth signal detection. In order to select optimal parameters for the wavelet filter, a two-step optimization process is proposed. Minimal Shannon entropy is used to optimize the Morlet wavelet shape factor. A periodicity detection method based on singular value decomposition (SVD) is used to choose the appropriate scale for the wavelet transform. The signal de-noising results from both simulated signals and experimental data are presented and both support the proposed method.

Introduction

Rolling element bearing are of paramount importance to almost all forms of rotating machinery and are among the most common machine elements. Bearing failure is one of the foremost causes of breakdowns in rotating machinery and such failure can be catastrophic, resulting in costly downtime. In order to prevent these kinds of failures from happening, various bearing condition monitoring techniques have been developed. Among them, vibration analysis has been used extensively due to its intrinsic advantage of revealing bearing failure [1], [12].

After nearly four decades of study of the bearing failure mechanism [2], [3], [4], the theoretical background of bearing failure modes has been covered quite comprehensively. The signature of a damaged bearing consists of exponentially decaying ringing that occurs periodically at the characteristic frequency [3]. The vibration signal of a defective bearing usually considers being amplitude modulated at the characteristic defect frequency. Matching the measured vibration spectrum with the defect characteristic frequency enables defect detection and enables diagnosis of the defective area.

As for the vibration signal of rolling element bearing, signal modulation effect and noise are two major barriers in incipient defect detection. Because of the amplitude-modulated effect, the spectrum of defect signals consists of a harmonic series of frequency components present at the bearing defect frequency with the highest amplitude around the resonance frequency [5]. To overcome this barrier, an effective signal demodulation technique should be developed. Most of the time vibration signals are collected with a vibration sensor installed on the bearing housing. The sensors are subject to collecting vibration responses from other mechanical components and noise sources. The inherent deficiency of the measuring mechanism introduces a great amount of noise to the signal. The signature of a defective bearing is spread across a wide frequency band and hence can easily become masked by noise and low frequency effects [6]. The weak signature, at the early stage of defect development, is even more difficult to detect. A signal enhancing method is needed to provide more evident information for incipient defect detection of rolling element bearings.

To solve the problem of modulation, a large variety of signal demodulation methods have been proposed. Eshleman [7] proposed a hardware-based signal envelope technique in which signals are passed through a capacitor to produce the demodulated time waveform. Fast Fourier Transform (FFT)-based Hilbert transform is the traditional method for deriving the signal envelope and has been widely used in roller bearing diagnostics [8]. More recently, the wavelet transform has been used for signal demodulation [5], [6], [9] and optimal band-pass filter design [10]. In summary, Hilbert transform and wavelet transform offer promising techniques for signal demodulation. However, those methods do not successfully address how to enhance the weak signature from a noisy signal and how to detect early stage defects.

The problem of signal de-noising has a strong connection to roller element bearing prognostics. De-noising and extraction of the weak signature are crucial to fault prognostics in which case features are often very weak and masked by noise. Prognostics is achieved by detecting the defect at its initial stage and alerting maintenance personnel before it develops into a catastrophic failure. The standard approach for extracting signals from a noisy background is to design an appropriate filter, which removes the noise components and at the same time, lets the desired signal go through unchanged. Based on noise type and application, different filters can be designed to conduct the de-noising [11]. However, for a situation where the noise type and frequency range are unknown, traditional filter design could become a very challenging task. Therefore, research is focused on finding alternative methods. The wavelet transform has been widely used in signal de-noising due to its extraordinary time-frequency representation capability [13], which is discussed in detail later in this paper. Traditionally, most of the signal de-noising approaches are dealing with detecting smooth curves from the noisy raw signals. However, the vibration signal from faulty mechanical components, such as gears and bearings, are more like impulses, instead of smooth and continuous curves. This unique feature constrains the application of conventional signal de-noising method. A de-noising method based on Morlet wavelet analysis is proposed and applied to the feature extraction of gearbox vibration signals [21]. This method seeks optimal wavelet filters that only yield the largest kurtosis value for the transformed signal, whereas the periodicity of the signal is not addressed.

In this paper, the performance of wavelet decomposition-based de-noising and wavelet filter-based de-noising methods are compared based on signals from mechanical defects. The comparison results reveal that the wavelet filter is more suitable and reliable to detect weak and impulse-like signatures of mechanical defect signals, whereas the wavelet decomposition de-noising method can achieve satisfactory results on smooth signal detection. In order to select the optimal parameters for the wavelet filter, a two-step optimization process is proposed. Minimal Shannon entropy is used as a criterion to optimize the shape factor of a Morlet wavelet. A periodicity detection method based on Singular Value Decomposition (SVD) is used to choose the appropriate scale for the wavelet transform. The signal de-noising results from both simulated signals and the experimental data are presented and both support the proposed method.

The remaining sections of this paper are organized as follows: In Section 2, the concept of a wavelet transform is reviewed. In Section 3, the wavelet decomposition-based de-noising method is discussed in detail. A comparison study is presented using two sets of simulated signals. The results suggest that for impulse-like signals, wavelet decomposition-based de-noising method is not able to achieve a satisfactory level of performance. In Section 4, the Morlet wavelet filter and its underlying capability of detecting weak impulse signatures from a noisy background is discussed and demonstrated using simulated signals. In Section 5, the proposed method is validated using the data collected from bearing run-to-failure tests. The result demonstrates that by designing an optimal wavelet filter bearing defects can be detected at an early stage of development and therefore bearing prognostics is possible.

Section snippets

Wavelet transform

The wavelet is obtained from a single function ψ(a,b)(t) by translation and dilation:ψ(a,b)(t)=1aψ(t-ba),where a is the so-called scaling parameter, b is the time localization parameter and ψ(t) is called the “mother wavelet”. The parameters of translation bR and dilation a>0, may be continuous or discrete.

The wavelet transform of a finite energy signal x(t) with the analyzing wavelet ψ(t) is the convolution of x(t) with a scaled and conjugated wavelet:W(a,b)=1a-x(t)ψ*(t-ba)dt,where ψ*(t)

Wavelet decomposition-based de-noising

The underlying model for the noisy signal is basically of the following form:x(n)=s(n)+σw(n),n=0,1,N-1.In this simplest model, w(n) is standard Gaussian white noise, independent and identically distributed (i.i.d.), denoted by w(n)i.i.d.N(0,1), and σ is the noise level. The objective of de-noising is to suppress the noise part of the signal x(n) and to recover s(n). Theoretically, this is accomplished by reconstructing the signal from the noisy data such that the mean squared error between s(n

The principle of the wavelet filter

Another method to extract useful information from a noisy signal is the wavelet filter. An important property of the Fourier transform is that convolution in one domain corresponds to multiplication in the other domain. So Eq. (2) can take the following alternative form:W(a,b)=aF-1{X(f)ψ*(af)},where X(f) and ψ(f) are the Fourier transforms of x(t) and ψ(t), respectively, and F-1 denotes the inverse Fourier transform. Eq. (7) shows that the wavelet transform can also be considered as a special

Experimental setup

Most bearing diagnostics research involves studying the defective bearings recovered from the field, where the bearings exhibit mature faults, or from simulated or “seeded” damage. Simulated damages are typically induced by scratching or drilling the surface, introducing debris into the lubricant, or machining with an electrical discharge. Experiments using defective bearings have less capability to discover natural defect propagation in the early stages. In order to validate the wavelet filter

Conclusion and discussion

De-noising and extraction of the weak signature from the noisy signal are crucial to fault prognostics, in which case features are often very weak and masked by the background noise. Prognostics is achieved by detecting the defect at its initial stage and alerting the operator or maintenance personnel before the defect develops into a catastrophic failure.

The performance of traditional wavelet decomposition-based de-noising methods is greatly impacted by relative energy levels of signal

Acknowledgement

This research was funded by the National Science Foundation Industry/University Cooperative Research Center (NSF I/UCRC) on Intelligent Maintenance Systems (IMS) under Grant No. 0117518. Rexnord Technical Services, an IMS sponsor, provided the testing facility and run-to-failure expertise for this research.

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