Adaptive Wavelet Transform Method to Identify Cracks in Gears
EURASIP Journal on Advances in Signal Processing
Hindawi Publishing Corporation
Adaptive Wavelet Transform Method to Identify Cracks in Gears
Ales Belsak 0
Joze Flasker 0
Ling Shao
0 Laboratory for Computer Aided Engineering, Faculty of Mechanical Engineering, University of Maribor , Smetanova ulica 17, 2000 Maribor , Slovenia
Many damages and faults can cause problems in gear unit operation. A crack in the tooth root is probably the least desirable among them. It often leads to failure of gear unit operation. By monitoring vibrations, it is possible to determine the presence of a crack. Signals are, however, very noisy. This makes it difficult to define properties of individual components. Wavelet analysis is an effective tool for analysing signals and for defining properties. In this paper, a denoising method based on wavelet analysis, which takes prior information about impulse probability density into consideration, is used to identify transient information from vibration signals of a gear unit with a fatigue crack in the tooth root.
1. Introduction
The aim of maintenance is to keep a technical system (gear
unit) in the most suitable working condition, and its purpose
is to discover, to diagnose, to foresee, to prevent and to
eliminate damages. The purpose of modern maintenance,
however, is not only to eliminate failures but also to define
the stage of a potential danger of a sudden failure of
system operation. The aim of diagnostics is to define the
current condition of the system and the location, shape, and
reason of damage formation. The following diagnostic values
are used to define incorrect operation, the possibility and
location of damages, and the possibility of elimination of
these damages: different signals, condition parameters, and
other indirect signs. Identification of the form of damage is
based on deviations from the values typical of a faultless gear
system.
Gear units are often used in various industrial
applications. Consequently, it is of utmost significance to identify
fault symptoms of a gear unit at an early stage. It is vibration
signals that are primarily used to identify faults but they are
always complex and it is difficult to identify faults in gear
units on the basis of vibration signals. Acquired vibration
signals often contain a lot of noise. With too much noise,
the useful information is corrupted to such an extent that
it is impossible to establish the condition or that a wrong
conclusion is made.
A gear unit consists of elements enabling the
transmission of rotating movement. Although a gear unit is a complex
dynamic model, its movement is usually periodical; faults
and damages represent a disturbing quantity or impulse.
Local and time changes in vibration signals indicate the
disturbance [1, 2] and it is possible to expect time-frequency
changes [3]. This idea is based on kinematics and operating
characteristics [4, 5].
It is of key importance to apply effective methods for the
identification (extraction) of properties from noisy signals.
Wavelet analysis is one such effective tool. It is especially
suitable when it comes to processing nonstationary signals.
Local energy distributions in time domain and frequency
domain are typical of transient property components of
vibration signals, which resemble a wavelet function. It is
possible to use wavelet functions to detect transient property
components due to similar structures.
It is possible to apply wavelets to extract features and
purge noise. Matching pursuits by Mallat [6] and
softthreshold denoising by Donoho and Johnstone [7, 8] are
among such procedures. Threshold in the wavelet domain
is used for threshold denoising. It is possible to present
that this is asymptotically almost optimal for many signals,
which have been corrupted by additive white Gaussian noise.
However, feature components of many mechanical dynamic
signals consist of impulse components. This method,
however, has not been proved effective for impulse component
extraction. Smoothness of the signal that will be isolated
is assumed by all previously mentioned methods, based on
orthogonal wavelet transforms. The transient components,
which are treated as noise, vary quickly. Some of these
methods result in an even greater smoothness than in
case of the original signal. Consequently, existing denoising
methods are not suitable for vibration analysis of signals
produced by gears as impulses that need to be isolated
are not smooth. For threshold denoising, Morlet wavelet is
used, and similarity between the Morlet wavelet and impulse
is applied. If nonorthogonal wavelet transform is used,
this does not ensure that, after the transform, independent
and identically distributed noise retains this characteristic
on each scale. After nonorthogonal wavelet transforms,
statistical noise attributes become different as rules that apply
for thresholding when orthogonal wavelet transforms are
used are not suitable for thresholding when nonorthogonal
wavele (...truncated)