Application of an impulse response wavelet to fault diagnosis of rolling bearings

doi:10.1016/j.ymssp.2005.09.014

Mechanical Systems and Signal Processing

Volume 21, Issue 2, February 2007, Pages 920-929

https://doi.org/10.1016/j.ymssp.2005.09.014 Get rights and content

Abstract

To target the characteristic of roller bearing fault vibration signals, the impulse response wavelet is constructed by using continuous wavelet transform to extract the feature of fault vibration signals, based on which two methods namely scale-wavelet power spectrum comparison and auto-correlation analysis of time-wavelet power spectrum are proposed. The analysis results from roller bearing vibration signals with out-race or inner-race fault show that the two proposed methods can detect the faults of roller bearing and identify fault patterns successfully.

Section snippets

Introductions

Wavelet transform is a time-frequency signal analysis method which is put forward in the recent years and has been widely used and developed. It has the local characteristic of time-domain as well as frequency-domain and its time-frequency window is changeable. In the processing of non-stationary signals it presents better performance than the traditional Fourier analysis. Hence, wavelet transform has many applications in rolling bearing fault diagnosis [1], [2], [3], [4], in which the binary

Continuous wavelet transform

Suppose function $ψ (t) \in L^{2} (R) \cap L (R)$ and $\hat{ψ} (0) = 0$ , and then according to the following formula construct the function group ${ψ_{a, b} (t)}$ $ψ_{a, b} (t) = | a |^{- 1 / 2} ψ (\frac{t - b}{a}) a, b \in R, a \neq 0$ which is called the analyzing wavelet or continuous wavelet, here ψ is named basic wavelet or mother wavelet and its Fourier transform is $\hat{ψ} (ω)$ . Besides a represents the scale parameter and b represents the orientation parameter.

The continuous wavelet transform of the function with finite energy $f (t) \in L^{2} (R)$ about $ψ (t)$ is defined as [10] $W_{f}$

The selection of wavelet-base function

When operating a roller bearing with local faults, the impulse impact response is generated. Because the impulse is a sort of transient excitation, the resonance of the bearing system natural frequency would arise. Suppose the delivery channel between the fault impact position and the fixed location of the sensor is changeless and take the rolling bearing as a system and its unit-impulse response function is $h (t)$ , then the vibration signal picked up by the sensor is as follows [11]: $x (t) = \sum_{k = 0}^{\infty} d_{k} h$

Scale-wavelet power spectrum comparison and its application

According to formula (3), $| W_{f} (a, b) |^{2} / C_{ψ} a^{2}$ can be regarded as the power density function on plane (a,b), that is, $| W_{f} (a, b) |^{2} Δ a Δ b / C_{ψ} a^{2}$ gives the power which has scale a and time b as the center, Δa as the scale interval and Δb as the time interval [7]. Hence formula (3) can be expressed as follows: $\int_{R} | f (t) |^{2} d t = \frac{1}{C_{ψ}} \int_{R} a^{- 2} E (a) d a$ $E (a) = \int_{R} {| W_{f} (a, b) |}^{2} d b .$

Formula (9) gives the power value of function $f (t)$ with scale a. Namely it gives the power critical density function with a different scale a, and function

Time-wavelet energy spectrum autocorrelation analysis method and its applications

Formula (3) can be expressed as follows: $\int_{R} | f (t) |^{2} d t = \int_{R} E (b) d b,$ where $E (b) = \frac{1}{C_{ψ}} \int_{R} | W_{f} (a, b) |^{2} / a^{2} d a .$

$E (b)$ gives the distribution of all the energies of signal in time axis and is called the time-wavelet power spectrum. Then the following formula (12) gives the distribution of vibration signal energy along with time in the integrating range of scale (frequency) a: $E^{'} (b) = \frac{1}{C_{ψ}} \int_{a_{1}}^{a_{2}} | W_{f} (a, b) |^{2} / a^{2} d a .$ $E^{'} (b)$ integrates all the energy of vibration signal in the local frequency band from scale (frequency) $a_{1}$ to

Conclusion

Aiming at the characteristics of the vibration signal of rolling bearing with fault, the impulse response wavelet is constructed to extract the fault feature in this paper, based on which two fault diagnosis methods based on continuous wavelet transform are proposed which are called scale-wavelet energy spectrum relative method and time-wavelet energy spectrum autocorrelation analysis method, respectively. Furthermore, the two methods are applied to the roll bearing fault diagnosis. The main

Acknowledgments

The support for this research under Chinese National Science Foundation Grant (No. 50275050) is gratefully acknowledged.

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Application of an impulse response wavelet to fault diagnosis of rolling bearings

Abstract

Section snippets

Introductions

Continuous wavelet transform

The selection of wavelet-base function

Scale-wavelet power spectrum comparison and its application

Time-wavelet energy spectrum autocorrelation analysis method and its applications

Conclusion

Acknowledgments

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing

NDT&E International

Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis

Journal of Sound and Vibration