CN106384076A - Sobel operator Wigner-Hough transform based gear fault feature extraction method - Google Patents
Sobel operator Wigner-Hough transform based gear fault feature extraction method Download PDFInfo
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- CN106384076A CN106384076A CN201610746921.1A CN201610746921A CN106384076A CN 106384076 A CN106384076 A CN 106384076A CN 201610746921 A CN201610746921 A CN 201610746921A CN 106384076 A CN106384076 A CN 106384076A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/08—Feature extraction
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/02—Preprocessing
- G06F2218/04—Denoising
Abstract
The invention discloses a Sobel operator and Wigner-Hough transform based gear fault feature extraction method, which comprises the steps of (1) inputting a gear fault signal S(t); (2) calculating to acquire Wigner-Ville distribution of the gear fault signal; (3) using the Wigner-Ville distribution acquired in the step (2) to act as an image, and performing edge detection by using a Sobel operator firstly; and then (4) extracting fault signal features through Hough transform. According to the invention, a time-frequency spectrum of the gear fault signal is regarded as a two-dimensional image, analysis and state recognition are performed by applying image processing, the fault diagnosis effect is good, and the signal detection result is more reliable.
Description
Technical field
The present invention relates to gear distress feature detection techniques field is and in particular to a kind of be based on Sobel operator and Wigner-
The Gear Fault Feature Extraction method of Hough transform.
Background technology
Time frequency analysis, due to having the localised information of time domain and frequency domain simultaneously, have become as the master of research non-stationary signal
Want instrument, be also the common method in current device fault diagnosis, such as wavelet analysises, Wigner-Ville distribution and nearest
Hilbert time-frequency spectrum method for expressing that exhibition is got up etc., has obtained widely studied and application in field of diagnosis about equipment fault.Event
The time-frequency spectrum of barrier signal regards two dimensional image as, then the Hough transform in image procossing is applied to fault diagnosis, is such as based on
The fault signature extracting method of Wigner-Hough conversion is also employed.But when signal to noise ratio is relatively low, Wigner-Hough becomes
The time-frequency spectrum changed can be flooded by noise it is difficult to the feature extraction of complete pair signals.
Content of the invention
It is stranded for Wigner-Hough conversion Gear Fault Feature Extraction in the case of low signal-to-noise ratio in above-mentioned prior art
Difficult deficiency, it is an object of the invention to provide the gear distress feature of a kind of combination Sobel operator and Wigner-Hough conversion
Extracting method.
For achieving the above object, the technical solution used in the present invention is：Based on Sobel operator and Wigner-Hough conversion
Gear Fault Feature Extraction method, comprise the steps：
（1）Input gear fault-signalS(t)；
（2）It is calculated the Wigner-Ville distribution of gear distress signal；
（3）Step（2）The Wigner-Ville distribution obtaining, as image, first carries out rim detection with Sobel operator；
（4）Again fault-signal feature is extracted by Hough transform.
Above-mentioned Wigner-Ville distribution（Abbreviation WVD）It is to apply a kind of bilinearity time-frequency distributions, for
Gear distress signalS(t), its Wigner-Ville distribution is defined as：
（Formula one）.
WVD has preferable time-frequency concentration class to simple component linear FM signal, but because WVD is bilinear, is dividing
During analysis multicomponent data processing, cross term, impact detection to actual signal between signal, occur.Therefore combine Hough transform, will believe
Number treatment technology is combined with image processing techniquess formation Wigner-Hough conversion, then analytic signalS(t) Wigner-
Hough transform is：（Formula two）；
It is then converted to the polar form shown in Fig. 1, expression formula is
（Formula three）；
Above formula formula three shows, if S (t) is parameter be f and g linear FM signal, integrated value is maximum；As parameter drift-out f
During with g, integrated value reduces rapidly, therefore to certain linear FM signal, can be corresponding after Wigner-Hough conversion
Peak value in parameter (f, g) place；And cross term will be weakened by integration.
Above-mentioned Sobel operator is the form of filter operator, it is possible to use fast convolution function extracts image border, simply
Effectively.For digital picture { f (i, j) }, Sobel operator is defined as follows：
A ( i, j) = │f ( i-1, j -1) + 2 f ( i-1, j) +
f ( i-1, j +1) ] - [ f ( i + 1, j - 1) +
2f ( i + 1, j) + f ( i + 1, j + 1) ] │ （Formula four）；
B (i, j) = │f ( i-1, j-1) + 2 f ( i, j-1) +
f ( i + 1, j-1) ] - [ f ( i-1, j + 1) +
2f ( i, j + 1) + f ( i + 1, j + 1) ] │ （Formula five）.
Then S (i, j)=max (A (i, j), B (i, j)) or S (i, j)=A (i, j)+B (i, j).Wherein A detection level side
Edge, B detects vertical edge, and the element in expression formula is the weighter factor of respective element.Choose suitable thresholding η, sentence as follows
Disconnected：If S (i, j)>η, then (I, j) it is marginal point, { S (i, j) } is edge image, the relation overflowed due to data, this edge
Image generally can not directly use, and use is then the image being made up of marginal point and background dot, therefore is bianry image.Directly
Make the image border that Sobel operator obtains relatively rough, need to be refined.Herein in order to obtain the detection edge refining, right
Sobel operator is improved, by the think of of the non-maxima suppression in Canny edge detection algorithm and morphology attended operation
Want to introduce Sobel operator.The traditional non-maxima suppression method of Canny operator, simply can be described as target pixel points
Gradient magnitude M (i, the j) gradient magnitude with the vicinity points at two ends on gradient magnitude direction respectivelyM'1(i,j)、M'2
(i,j) contrasted, ifM(i,j)>M'2(i,j) andM(i,j)>M'1(i,j), thenM(i,j) keep not
Become, otherwiseM(i,j)=0, realizes non-maxima suppression process.Morphology carried out out using omnidirectional structuring elements in connecting-
Close and close-open filtering, the then operation result pointwise to open-close takes gray scale maximum, to filter black noise, and to closing-open
Operation result pointwise take minimum gray value, to filter white noise.
Above-mentioned Hough transform is mainly used to detection of straight lines, (x,y) in plane, straight lineLCan be with below equation come table
Show：, 0≤θ≤π（Formula six）；
In formula：ρFor the distance of initial point to straight line,θFor vertical line andxAngle between axle.By the mapping of formula six, (x,y
) in plane every bit (ρ,θ) parameter space one sine curve of correspondence.(ρ,θ) in parameter space, on straight line L
The corresponding curve of each point can intersect at a point, and the coordinate of this point correspond to the parameter of straight line L.In parameter space, by long-pending
Branch forms a spike in point of intersection, such Hough transform (x,y) to be converted to parameter to the detection of straight line in plane empty
Between in detection to peak point.
Compared to existing technologies, beneficial effects of the present invention：1st, by regarding the time-frequency spectrum of gear distress signal as two
Dimension image, application image processes knowledge and is analyzed and state recognition, and fault diagnosis effect is good；2nd, pass through with Sobel operator first
Edge check is carried out to time-frequency distributions, is then converted with Hough again and extract fault-signal feature, signal detecting result more may be used
Lean on；3rd, the Wigner-Hough conversion based on Sobel operator preferably inhibits WVD to produce in analysis multicomponent data processing
Cross term, preferably inhibits effect of noise especially in the case of low signal-to-noise ratio, and the fast operation of algorithm, very suitable
The feature extraction of fault-signal in the case of conjunction high-volume data and low signal-to-noise ratio.
Brief description
Fig. 1 is Hough transform schematic diagram.
Fig. 2 is when emulation signal adds signal to noise ratio respectively for 0dB, 10dB and -10dB noise, using WHT, SPWD-
The comparison diagram of the Hough transform and the inventive method feature extraction to emulation signal；Wherein（a）For adding signal to noise ratio 10dB noise
Diagram,（b）For adding the diagram of signal to noise ratio 0dB noise,（c）For adding the diagram of signal to noise ratio -10dB noise.
Fig. 3 is the time domain beamformer of change speed gear box vibration signal during analysis of experiments.
Fig. 4 is Fourier spectrometry during analysis of experiments and the characteristic spectrum after the inventive method handling failure signal, wherein（a）
The result processing for Fourier spectrometry,（b）The result processing for the inventive method.
Fig. 5 is feature extraction during analysis of experiments with WHT method, the inventive method and the gear distress signal not plus before damage
Comparison diagram, wherein（a）For the extraction result of WHT method,（b）The inventive method extracts result,（c）Damage front extraction knot for not adding
Really.
Specific embodiment
In conjunction with specific embodiment, next the invention will be further elaborated.
Embodiment one
The first step：Input gear fault-signal S (t)；
Second step：It is calculated the Wigner-Ville distribution of gear distress signal：First the WVD of signal S (t) is defined as：,（Formula one）
3rd step：Using the Wigner-Ville distribution obtaining as image { f (i, j) }, first carry out edge inspection with Sobel operator
Survey：For image { f (i, j) }, A (i, j) and B (i, j) is the result after holding Sobel operator, if S (i, j)=max is (A (i, j), B
(i, j)) or S (i, j)=A (i, j)+B (i, j), wherein A detection level edge, B detects vertical edge；Choose suitable thresholding η,
Make following judgement：If S (i, j)>η, then (I, j) it is marginal point, { S (i, j) } is edge image；
4th step：Again fault-signal feature is extracted by Hough transform：After rim detection, the Wigner-Hough of S (t)
It is transformed to：
；（Formula two）
It is then converted into polar form as shown in Figure 1, expression formula is：
；（Formula three）
Fault-signal feature is extracted by formula three.
Emulation experiment
For proving the effectiveness of the inventive method, the emulation signal of gear distress is verified.According to gear distress signal
Feature, if the emulation signal of gear distress is：
；（Formula seven）
In formula seven：X kForkThe amplitude of rank meshing frequency harmonic component,HPolynomial Terms included in formula seven
Number,φ kForKThe initial phase of rank meshing frequency harmonic component,f zTurn frequency for axle,ZFor number of gear teeth；d k(t) andb k(t)
It is respectivelyKThe amplitude of rank meshing frequency harmonic component and phase modulation function.When local fault in gear, fault tooth
Wheel engages once with axle each rotation, therefored k(t) andb kT () is to turn frequencyf zAnd its frequency multiplication is the cycle letter of repetition rate
Number,i(t) it is noise function.In emulation signal hypothesis formula sevenH=2,x 1=1.0,x 2=0.4,d 1(t)=0.2sin
(2πf zT),d 2(t)=0.2sin (4 πf zT),b 1(t)=0.2sin (2 πf zT),b 2(t)=0.2sin (4 πf zT),φ 1=φ 2=π/6, z=18,f z=20, sample frequency is 4096Hz, and sampling number is 1000.
Fig. 2 compare emulation signal add respectively signal to noise ratio be 0dB, 10dB and -10dB noise when, using WHT, SPWD-
The feature extraction to emulation signal of Hough transform and the inventive method.From Fig. 2（a）In as can be seen that more a height of in signal to noise ratio
During 10dB, three kinds of methods all can correctly obtain the feature of two FM signal, but also some are significantly distinguished：Due to cross term
Impact, directly use WHT when, extract in figure burr more；SPWD- Hough transform is extracted in figure burr and has been suppressed, but
Concentration decreases；And the extraction in figure in the inventive method, image understands clean this two signals that indicate, accurately
Degree and aggregation are all better than first two situation.From Fig. 2（c）In as can be seen that signal to noise ratio than relatively low for -10dB when, due to hand over
Fork item and effect of noise, cannot get the basic feature of signal after directly using WHT, occur in that many puppet peaks, such as Fig. 2（c）'s
Shown in left figure；Signal is carried out after SPWD, carry out feature extraction with Hough conversion again, such as Fig. 2（c）Middle figure shown in although
SPWD inhibits cross term to a great extent, but because the interference ratio of noise is larger, still None- identified goes out signal characteristic；Adopt
With the inventive method, signal is carried out after WVD, first carry out rim detection with improving Sobel operator, then pass through Hough transform
Extract straight line, obtain as Fig. 2（c）Effect shown in right figure.By Fig. 2（c）Right figure can be seen that although comparing Fig. 2（a）The effect of right figure
Fruit will differ from, but it is already possible to be clearly seen that two impacts in the case of weak signal to noise ratio, it can be seen that the present invention
Method can suppress the interference of cross term in WVD effectively, and is also reliable for the signal detecting result of low signal-to-noise ratio.
Additionally, also the operation time under different signal to noise ratios compares research to 3 kinds of methods, the results are shown in Table 1.
Table 1：The operation time contrast of 3 kinds of methods
Can be seen that under identical data length and signal to noise ratio from table 1, after improving Sobel operator Edge check,
WHT conversion significantly shortens operation time, and efficiency improves nearly 2 orders of magnitude.As signal to noise ratio is dropped to by 20 dB
During -20 dB, directly carry out WHT run time be from 0.381 s about increase to 2.564s, and through improving
WHT run time after Sobel operator filtering is to increase to 0.048s from 0.013 s, and calculating speed is greatly improved, and
Method velocity variations amplitude very little after improvement.It can be seen that, the inventive method is especially suitable for high-volume data and low signal-to-noise ratio situation
The real-time characteristic of lower fault-signal extracts.
Analysis of experiments
For verifying effectiveness in Gear Fault Feature Extraction for the inventive method further, to the tooth that there is tooth root crack fault
Wheel carries out analysis of experiments.The number of teeth of gearz=15, modulusm=2mm, turn frequency of gear shaftf r=480r/min, ratcheting frequencyf z=120Hz, signal sampling frequencies are 1kHz, and sampling number is 1024.In some root portion of gear, manufactured with electric spark
One 0.1mm width and the deep damage of 3mm, simulate fissure.In fault signal analysis, if there is tooth root fatigue crack in gear
Etc. fault, then when this gear engages, the amplitude of vibration signal and phase place change, and produce amplitude and phase-modulation.Fault
The vibration signal of gear often shows as the modulation to meshing frequency and its frequency multiplication for the gyrofrequency, is formed to engage on spectrogram
Centered on frequency, two sidebands being spacedly distributed.Therefore, Gear Fault Diagnosis are substantially the identification of sideband.
It is the time domain waveform of change speed gear box vibration signal shown in Fig. 3, there it can be seen that periodically pulsing signal is nearly all
It is submerged among powerful background noise, bring very big difficulty to the feature extraction of fault-signal.Fig. 4（a）Illustrate signal
Fourier spectra it is clear that disturb to extract fault-signal bring very big trouble.For contrasting, Fig. 4（b）Give with this
Signal envelope after inventive method process.Fig. 5 gives the design sketch extracting fault signature with WHT method and the inventive method.
In Fig. 5（a）In, when directly removing to extract fault signature with WHT method, due to the impact of noise and cross term, burr is very
Many and amplitude is very big, this has just had a strong impact on the diagnosis of fault.Fig. 5（b）It is the characteristic pattern being extracted with the inventive method.For doing ratio
Relatively, Fig. 5（c）Give the characteristic pattern extracting before adding crack fault.In Fig. 5（b）In polar coordinate (ρ,θ) space, right
Answer the peak value of frequency（Including 8 hertz of turn frequency, the harmonic wave of the meshing frequency of gear：240 hertz, 360 hertz and they around
Modulating frequency）Apparent.It can be seen that, Fig. 4（b）And Fig. 5（b）All clearly illustrate the feature of fault-signal, for further
Fault diagnosis provide condition.This also further demonstrate that the inventive method also can be effectively in the case of low noise ratio
Extract gear distress feature.
Claims (1)
1. the Gear Fault Feature Extraction method based on Sobel operator and Wigner-Hough conversion, comprises the steps：
（1）Input gear fault-signalS(t)；
（2）It is calculated the Wigner-Ville distribution of gear distress signal；
（3）Step（2）The Wigner-Ville distribution obtaining, as image, first carries out rim detection with Sobel operator；
（4）Again fault-signal feature is extracted by Hough transform.
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| CN110542557A (en) * | 2019-08-21 | 2019-12-06 | 中国一拖集团有限公司 | method for rapidly analyzing periodic fault characteristics of large data of machine tool driven by image integration |
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