CN109080661A - It is a kind of that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD - Google Patents
It is a kind of that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD Download PDFInfo
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- B61K9/00—Railway vehicle profile gauges; Detecting or indicating overheating of components; Apparatus on locomotives or cars to indicate bad track sections; General design of track recording vehicles
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Abstract
The invention discloses a kind of track waves to grind fault detection method, is based on EEMD Energy-Entropy and WVD time frequency analysis, comprising the following steps: carries out EEMD decomposition to the initial acceleration signal of collected vehicle axle box vibration, obtains multiple IMF component signals；Calculate the EEMD energy of each IMF component signal and the signal gross energy of all IMF component signals；The EEMD Energy-Entropy of IMF component signal is calculated according to the EEMD Energy distribution of IMF component signal；Carry out track wave and grind fault diagnosis: by EEMD energy entropy compared with given threshold, if EEMD energy entropy is not less than given threshold, there is no waves to grind failure for track；If EEMD energy entropy is less than threshold value, there is wave mill failure at this time, then enter next step；WVD time frequency analysis is carried out to each IMF component signal respectively, and by the result linear superposition of WVD time frequency analysis, obtains the time-frequency figure of vibration signal；Location of fault is ground according to time-frequency figure positioning wave, and estimates the wave mill length of wave mill failure.The feature that the detection method is simple, real-time is good.
Description
Technical field
The invention belongs to city underground rail deformation detections and safe early warning technical field, and in particular to one kind is based on EEMD
The track wave of Energy-Entropy and WVD grind fault detection method.
Background technique
Rail traffic is recruited as the key one for solving urbanization transport development, is brought convenience for people's trip.City at present
Rail traffic is just obtaining the support and propulsion of country energetically, and more and more cities start planning construction, and total kilometrage has reached
1000 kilometers.In a few years to be developed, the numerous city in China will all possess subway, the new development chapter of opening track traffic,
China forms perfect trip transportation network, provides convenient and fast mode of transportation for city dweller.But track circuit is attended by simultaneously
The lasting stream of people expanded and increase sharply, safety of urban transit problem is increasingly prominent to be come out.
Track is as the key component in the railway system, when vehicle is when operation, ensures vehicle safety row always
The direction for sailing and guide train advance subjects whole weight of vehicle.Due to track and take turns between due to for a long time
Rubbing action, cause raceway surface irregularity, abrasion even depressed phenomenon occur, and serious track irregularity will lead to
Active force between wheel track sharply increases, and can not only generate serious wheel track noise, influences the riding comfort of train, and
It will be greatly reduced the active time of train and rail system components, or even will cause driving accident.
At present the excessively inside and outside detection method to rail corrugation first is that inertia method is led to using the inertial reference of accelerometer
It crosses and quadratic integral acquisition irregularity value is carried out to obtained large-scale rail inspection train axle box acceleration signal, such as: Britain
RCA wave mill analysis vehicle, China's rail wave abrasion dynamic detection system RCIU-1 that Railmeasurement company develops etc..
The detection accuracy of this method can reach micron order, but its equipment cost is high, less adapts in track Daily Round Check.It is another
The more common detection method of kind is straight ruler, such as HYGP-3 rail flatness measuring instrument.Its measuring principle is simple, but operates
This large labor intensity and detection efficiency is low.
Summary of the invention
The present invention provides a kind of rail based on EEMD Energy-Entropy and WVD based on EEMD Energy-Entropy and WVD time frequency analysis
Road wave grinds fault detection method, has the characteristics that method is simple, real-time is good.
In order to solve the above technical problems, the invention adopts the following technical scheme:
It is a kind of that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD, when being based on EEMD Energy-Entropy and WVD
Frequency analysis, comprising the following steps:
S1: EEMD decomposition is carried out to the initial acceleration signal of collected vehicle axle box vibration, obtains multiple IMF components
Signal；
S2: the signal of the EEMD energy and multiple IMF component signals that calculate each IMF component signal is total
Energy；
S3: the EEMD Energy-Entropy of IMF component signal is calculated according to the EEMD Energy distribution of IMF component signal；
S4: it carries out track wave and grinds fault diagnosis: by the EEMD energy entropy compared with given threshold, if the EEMD energy
It measures entropy and is not less than the given threshold, that is, can determine that track, there is no waves to grind failure；If the EEMD energy entropy is less than institute
Threshold value is stated, that is, can determine that track, there are waves to grind failure, then enters next step S5；
S5: carrying out WVD time frequency analysis each described IMF component signal respectively, and by the result line of WVD time frequency analysis
Property superposition, obtain the time-frequency figure of vibration signal；
S6: grinding location of fault according to time-frequency figure positioning wave, and estimates the wave mill length of wave mill failure.
Further, step S1 specifically includes the following steps:
S11: to acceleration signal x0(t) the effective white Gaussian noise n of addition inj(t) decomposed signal y is obtainedj(t), specifically
Formula are as follows:
yj(t)=x0(t)+k*nj(t) (j=1,2,3,4 ... n) (1)
Wherein, x0It (t) is initial acceleration signal, k is the amplitude coefficient of effective white Gaussian noise, and n is having for addition
The total quantity of the white Gaussian noise of effect；
S12: by decomposed signal yj(t) it decomposes and obtains the jth group IMF phasesequence component c being made of m phasesequence componentji(t),
Wherein, i=1,2,3,4 ... m, and m is the integer not less than 1；
Its specific decomposition step is as follows:
A: decomposed signal y is calculatedj(t) maximum and minimum point, and by decomposed signal yj(t) maximum point existing for
It is fitted respectively with minimum point and respectively obtains coenvelope line yj(up)(t) and lower envelope line yj(low)(t)；
Wherein, cubic spline interpolation refers to an a series of smooth curve by shape value points, mathematically by solving three
Bending Moment Equations group obtains the process of curvilinear function group.
B: according to coenvelope line, lower envelope line computation average value curve mj(t), specific formula are as follows:
C: following one sequences h of formulas Extraction are utilizedj(t)
hj(t)=x0(t)-mj(t) (3)
If sequences hj(t) it is unsatisfactory for IMF condition, then decomposition step terminates, and enters step S13；
If sequences hj(t) meet IMF condition, then by the sequences hj(t) it is denoted as i-th of phasesequence component c of the j groupji(t),
And enter next step d；
D: by the phasesequence component h of extractionji(t) from decomposed signal yj(t) in after removal, i.e., by (yj(t)-hji(t)) value
Again it is assigned to yj(t) after, step a~c is repeated, new phasesequence component c is obtainedj(i+1)(t)；
S13: as j < n, different effective white Gaussian noises is added to initial acceleration signal, and repeat the above steps
S11~S12 can get the c of n group phasesequence component compositionji(t)；
S14: the average value of the phasesequence component of every group of corresponding sequence in the n group phasesequence component is calculated, m decomposition can be obtained
Mean valueThe decomposition mean value is the IMF component signal
Further, in step a, using using cubic spline interpolation to the maximum of decomposed signal and minimum into
Row fitting.
Further, effective white Gaussian noise total quantity n is no less than 50.
Further, step S2 specifically includes the following steps:
S21: the energy value E of IMF component signal is calculated separately using following formulai
Wherein, AiIt (t) is the IMF component amplitude maximum value, ti-1It is the starting of IMF component, tiIt is IMF dwell time, m is
The quantity of IMF component signal；
S22: signal total energy value is calculated.
Further, step S3 specifically includes the following steps:
S31: the energy value E of each IMF component signal is calculatediProbability in signal total energy value E；
S32: Probability p is utilizediCalculate the EEMD Energy-Entropy of the IMF component signal.
Further, step S5 specifically includes the following steps:
Obtain the IMF component signalInstantaneous auto-correlation function, and Fourier is done to the instantaneous auto-correlation function
Transformation, obtains instantaneous time-frequency function WDi(t,ω)；
By each WDi(t, ω) carries out linear superposition, obtains the WVD time-frequency figure WD (t, ω) of signal x (t).
Further, step S6 medium wave mill position and wave mill length can be determined according to such as under type:
According to the frequency concentrated area in time-frequency figure, positioning track wave grinds the specific location of failure；And according to time-frequency figure
Area estimation has the wavelength of wave mill failure in frequency set.
Compared with prior art, the invention has the benefit that
It is of the invention that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD, based on EEMD Energy-Entropy and
WVD time frequency analysis can quickly position wave mill abort situation fastly, and estimate the wave mill length of wave mill failure, judge wave mill event
The severity of barrier is safeguarded so as to preferably grind failure according to wave.The track wave based on EEMD Energy-Entropy and WVD
The real-time of mill fault detection method is good, detection efficiency is high, easy to operate, is suitble to track maintenance repair.
Detailed description of the invention
Technology of the invention is described in further detail with reference to the accompanying drawings and detailed description:
Fig. 1 is the flow chart of the present invention that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD；
Fig. 2 is that the present invention emulates to obtain 50mm wavelength 0.04mm depth of convolution axle box vibration acceleration signal by SIMPACK；
Fig. 3 is that 50mm wavelength 0.04mm depth of convolution EEMD of the present invention decomposes IMF component energy distribution map；
Fig. 4 is that 50mm wavelength 0.04mm depth of convolution EEMD decomposes IMF component energy entropy distribution map；
Fig. 5 is 50mm wavelength 0.04mm depth of convolution signal time-frequency figure of the present invention；
Fig. 6 is 50mm wavelength 0.04mm depth of convolution signal time-frequency amplitude figure of the present invention.
Specific embodiment
Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings, it should be understood that preferred reality described herein
Apply example only for the purpose of illustrating and explaining the present invention and is not intended to limit the present invention.
Fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD the invention discloses a kind of, such as Fig. 1-figure institute
Show, be based on EEMD Energy-Entropy and WVD time frequency analysis, comprising the following steps:
S1: carrying out EEMD decomposition to the initial acceleration signal (abbreviation vibration signal) of collected vehicle axle box vibration,
Obtain multiple IMF component signals；Wherein, it before carrying out EEMD decomposition to initial acceleration signal, needs first to the acceleration of acquisition
Signal is filtered.
Multiple IMF component signals can be specifically obtained by following steps:
S11: to acceleration signal x0(t) the effective white Gaussian noise n of addition inj(t) decomposed signal y is obtainedj(t), specifically
Formula are as follows:
yj(t)=x0(t)+k*nj(t) (j=1,2,3,4 ... n) (1)
Wherein, x0It (t) is initial acceleration signal, k is the amplitude coefficient of effective white Gaussian noise, and n is having for addition
The total quantity of the white Gaussian noise of effect, it is preferred that n is not less than 50.
S12: by decomposed signal yj(t) it decomposes and obtains the jth group IMF phasesequence component c being made of m phasesequence componentji(t),
Wherein, i=1,2,3,4 ... m, and m is the integer not less than 1；
Its specific decomposition step is as follows:
A: decomposed signal y is calculatedj(t) maximum and minimum point, and use cubic spline interpolation by decomposed signal yj
(t) maximum point and minimum point existing for are fitted respectively respectively obtains coenvelope line yj(up)(t) and lower envelope line yj(low)(t)；
Wherein, cubic spline interpolation refers to an a series of smooth curve by shape value points, mathematically by solving three
Bending Moment Equations group obtains the process of curvilinear function group.
B: according to coenvelope line, lower envelope line computation average value curve mj(t), specific formula are as follows:
C: following one sequences h of formulas Extraction are utilizedj(t)
hj(t)=x0(t)-mj(t) (3)
If sequences hj(t) it is unsatisfactory for IMF condition, then decomposition step terminates, and enters step S13；
If sequences hj(t) meet IMF condition, then by the sequences hj(t) it is denoted as i-th of phasesequence component c of the j groupji(t),
And enter next step d；
D: by the phasesequence component h of extractionji(t) from decomposed signal yj(t) in after removal, i.e., by (yj(t)-hji(t)) value
Again it is assigned to yj(t) after, step a~c is repeated, new phasesequence component c is obtainedj(i+1)(t)；
S13: as j < n, different effective white Gaussian noises is added to initial acceleration signal, and repeat the above steps
S11~S12 can get the c of n group phasesequence component compositionji(t)；
S14: the average value of the phasesequence component of every group of corresponding sequence in the n group phasesequence component is calculated, m decomposition can be obtained
Mean valueThe decomposition mean value is the IMF component signal
In above-mentioned steps S11, the selection process of effective white Gaussian noise are as follows:
1) to initial acceleration signal x0(t) an arbitrary white Gaussian noise n is added ina(t) decomposed signal y is obtaineda
(t)；
2) decomposed signal y is calculateda(t) maximum and minimum point, and use cubic spline interpolation by decomposed signal yj
(t) maximum point and minimum point existing for are fitted respectively respectively obtains coenvelope line ya(up)(t) and lower envelope line ya(low)(t)；
3) according to coenvelope line, lower envelope line computation average value curve ma(t)；
4) first sequences h is extracteda(t), wherein ha(t)=x0(t)-ma(t)；
If sequences ha(t) it is unsatisfactory for IMF condition, the white Gaussian noise of the addition is invalid white Gaussian noise, need to be to initial
Acceleration signal adds new white Gaussian noise again, and is returned to step 1) and re-starts judgement；
If sequences ha(t) meet IMF condition, the white Gaussian noise added at this time is then an effective white Gaussian noise.
S2: the signal of the EEMD energy and multiple IMF component signals that calculate each IMF component signal is total
Energy；
Specifically includes the following steps:
S21: the EEMD energy value E of each IMF component signal of integral calculationi, specific formula is as follows:
Wherein, AiIt (t) is the IMF component amplitude maximum value, ti-1It is the starting of IMF component, tiIt is IMF dwell time, m is
The quantity of IMF component signal；
S22: the EEMD energy value of each IMF component signal is added up, and can acquire multiple IMF component letters
Number total energy value
S3: the EEMD Energy-Entropy of IMF component signal is calculated according to the EEMD Energy distribution of IMF component signal；
Specifically include following two step:
S31: the energy value E of each IMF component signal is calculatediProbability in signal total energy value E
S32: Probability p is utilizediCalculate the EEMD Energy-Entropy H of the IMF component signalEE, specific formula is as follows:
S4: it carries out track wave and grinds fault diagnosis: by the EEMD energy entropy compared with given threshold, if the EEMD energy
It measures entropy and is not less than the given threshold, that is, can determine that track, there is no waves to grind failure；If the EEMD energy entropy is less than institute
Threshold value is stated, that is, can determine that track, there are waves to grind failure, then enters next step S5；
S5: carrying out WVD time frequency analysis each described IMF component signal respectively, and by the result line of WVD time frequency analysis
Property superposition, obtain the time-frequency figure of vibration signal；It specifically includes:
Obtain the IMF component signalInstantaneous auto-correlation function, and Fourier is done to the instantaneous auto-correlation function
Transformation, obtains instantaneous time-frequency function WDi(t,ω)；
By each WDi(t, ω) carries out linear superposition, obtains the WVD time-frequency figure WD (t, ω) of signal x (t).
S6: location of fault is ground according to time-frequency figure positioning wave, and estimates wave mill length (namely wavelength) of wave mill failure, tool
Body can be determined according to such as under type:
The frequency concentrated area in time-frequency figure is found, which is failure-frequency section, according to failure frequency
Rate section can positioning track wave mill failure specific location；The wave of wave mill failure can be estimated according to the failure-frequency section simultaneously
It is long.
It is of the invention that fault detection method is ground based on the track wave of EEMD Energy-Entropy and WVD, based on EEMD Energy-Entropy and
WVD time frequency analysis can quickly position wave mill abort situation fastly, and estimate the wave mill length of wave mill failure, judge wave mill event
The severity of barrier is safeguarded so as to preferably grind failure according to wave.The track wave based on EEMD Energy-Entropy and WVD
The real-time of mill fault detection method is good, detection efficiency is high, easy to operate, is suitble to track maintenance repair.
This method is illustrated combined with specific embodiments below:
Embodiment 1:
In order to simulate actual trajcctorics state as far as possible, the mode that superposition ripple is ground in track spectrum carries out track and sets the present embodiment
It sets, when SIMPACK emulation experiment, sample frequency 1kHz, track length 95m, only there are wavelength 50mm waves at 65~-67m
The rail fault of deep 0.04mm only exists the vertical irregularity of track spectrum in other positions, and setting train running speed is 10m/s
Setting and other settings, obtain axle box Vertical Acceleration signal as shown in Figure 2.
EEMD decomposition is carried out to collected axle box vibration acceleration signal, obtains 11 IMF components and 1 res component.
Since res component is useless item, signal analysis is not influenced, therefore does not have to handle it；Decomposition is obtained each
A IMF component calculates separately its EEMD energy, obtains energy profile as shown in Figure 3.
According to the Energy distribution of IMF component, Energy-Entropy distribution map as shown in Figure 4 is obtained.And it can be counted according to energy entropy
The total entropy of EEMD for calculating IMF component is 0.2685.It is 0.6 according to fault-free emulation signal setting threshold value, the setting threshold value is big
In 0.2685, i.e. EEMD energy entropy is significantly less than threshold value, it is possible thereby to judge that there are waves to grind failure.
WVD analysis is carried out to IMF component respectively, and the IMF of each IMF component analysis result is subjected to linear superposition and is
The two-dimentional time-frequency figure and three-dimensional time-frequency amplitude figure shown in fig. 6 of signal as shown in Figure 5 can be obtained.
Find out from Fig. 5 and Fig. 6, frequency of occurrences concentrated area in figure, such as the region a in figure, and it is attached 65~67 meters of
Closely, frequency is essentially identical with emulation wave mill position substantially near 200Hz.Wavelength is ground for estimation wave, by region a micronization processes
Vibration amplitude is maximum at 199.8Hz.According to theory deduction, there is following relationships for wave mill wavelength and frequency:λ
Wavelength is ground for wave, f is frequency, and v is train driving speed.Wavelength X=50.05mm is calculated, the wavelength 50mm base with emulation setting
This is consistent.
Other contents of the present invention based on the track wave of EEMD Energy-Entropy and WVD mill fault detection method are referring to existing
There is technology, details are not described herein.
The above described is only a preferred embodiment of the present invention, be not intended to limit the present invention in any form, therefore
Without departing from the technical solutions of the present invention, according to the technical essence of the invention it is to the above embodiments it is any modification,
Equivalent variations and modification, all of which are still within the scope of the technical scheme of the invention.
Claims (8)
1. a kind of grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, it is characterised in that: it is based on EEMD energy
Entropy and WVD time frequency analysis, comprising the following steps:
S1: carrying out EEMD decomposition to the initial acceleration signal of collected vehicle axle box vibration, obtains multiple IMF component letters
Number；
S2: the EEMD energy of each IMF component signal and the signal total energy of multiple IMF component signals are calculated
Amount；
S3: the EEMD Energy-Entropy of IMF component signal is calculated according to the EEMD Energy distribution of IMF component signal；
S4: it carries out track wave and grinds fault diagnosis: by the EEMD energy entropy compared with given threshold, if the EEMD Energy-Entropy
Value is not less than the given threshold, that is, can determine that track, there is no waves to grind failure；If the EEMD energy entropy is less than the threshold
Value, that is, can determine that track, there are waves to grind failure, then enters next step S5；
S5: WVD time frequency analysis is carried out each described IMF component signal respectively, and the result of WVD time frequency analysis is linearly folded
Add, obtains the time-frequency figure of vibration signal；
S6: grinding location of fault according to time-frequency figure positioning wave, and estimates the wave mill length of wave mill failure.
2. according to claim 1 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In, step S1 specifically includes the following steps:
S11: to acceleration signal x0(t) the effective white Gaussian noise n of addition inj(t) decomposed signal y is obtainedj(t), specific formula
Are as follows:
yj(t)=x0(t)+k*nj(t) (j=1,2,3,4 ... n) (1)
Wherein, x0It (t) is initial acceleration signal, k is the amplitude coefficient of effective white Gaussian noise, and n is the effective height of addition
The total quantity of this white noise；
S12: by decomposed signal yj(t) it decomposes and obtains the jth group IMF phasesequence component c being made of m phasesequence componentji(t), wherein
I=1,2,3,4 ... m, and m is the integer not less than 1；
Its specific decomposition step is as follows:
A: decomposed signal y is calculatedj(t) maximum and minimum point, and by decomposed signal yj(t) maximum point and pole existing for
Small value point is fitted respectively respectively obtains coenvelope line yj(up)(t) and lower envelope line yj(low)(t)；
Wherein, cubic spline interpolation refers to an a series of smooth curve by shape value points, mathematically by solving three moments of flexure
Equation group obtains the process of curvilinear function group.
B: according to coenvelope line, lower envelope line computation average value curve mj(t), specific formula are as follows:
C: following one sequences h of formulas Extraction are utilizedj(t)
hj(t)=x0(t)-mj(t) (3)
If sequences hj(t) it is unsatisfactory for IMF condition, then decomposition step terminates, and enters step S13；
If sequences hj(t) meet IMF condition, then by the sequences hj(t) it is denoted as i-th of phasesequence component c of the j groupji(t), and enter
Next step d；
D: by the phasesequence component h of extractionji(t) from decomposed signal yj(t) in after removal, i.e., by (yj(t)-hji(t)) value is again
It is assigned to yj(t) after, step a~c is repeated, new phasesequence component c is obtainedj(i+1)(t)；
S13: as j < n, adding different effective white Gaussian noises to initial acceleration signal, and the S11 that repeats the above steps~
S12 can get the c of n group phasesequence component compositionji(t)；
S14: calculating the average value of the phasesequence component of every group of corresponding sequence in the n group phasesequence component, and m decomposition mean value can be obtainedThe decomposition mean value is the IMF component signal
3. according to claim 2 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: in step a, the maximum and minimum of decomposed signal are fitted using using cubic spline interpolation.
4. according to claim 2 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: effective white Gaussian noise total quantity n is no less than 50.
5. according to claim 1 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: step S2 specifically includes the following steps:
S21: the energy value E of IMF component signal is calculated separately using following formulai
Wherein, AiIt (t) is the IMF component amplitude maximum value, ti-1It is the starting of IMF component, tiIt is IMF dwell time, m is IMF points
Measure the quantity of signal；
S22: signal total energy value is calculated.
6. according to claim 1 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: step S3 specifically includes the following steps:
S31: the energy value E of each IMF component signal is calculatediProbability in signal total energy value E；
S32: Probability p is utilizediCalculate the EEMD Energy-Entropy of the IMF component signal.
7. according to claim 1 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: step S5 specifically includes the following steps:
Obtain the IMF component signalInstantaneous auto-correlation function, and Fourier transformation is done to the instantaneous auto-correlation function,
Obtain instantaneous time-frequency function WDi(t,ω)；
By each WDi(t, ω) carries out linear superposition, obtains the WVD time-frequency figure WD (t, ω) of signal x (t).
8. according to claim 1 grind fault detection method based on the track wave of EEMD Energy-Entropy and WVD, feature exists
In: step S6 medium wave grinds position and wave mill length and can be determined according to such as under type:
According to the frequency concentrated area in time-frequency figure, positioning track wave grinds the specific location of failure；And according to the frequency of time-frequency figure
Concentrated area estimates the wavelength of wave mill failure.
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| CN109532940A (en) * | 2018-11-06 | 2019-03-29 | 北京交通大学 | The fastener of high speed non-fragment orbit loosens degree detecting method |
| CN110015319A (en) * | 2019-03-13 | 2019-07-16 | 北京锦鸿希电信息技术股份有限公司 | Track wave grinds recognition methods, device, equipment and storage medium |
| CN110426005A (en) * | 2019-07-01 | 2019-11-08 | 中国铁道科学研究院集团有限公司节能环保劳卫研究所 | Rail in high speed railway wave based on IMF energy ratio grinds acoustics diagnostic method |
| CN113486874A (en) * | 2021-09-08 | 2021-10-08 | 西南交通大学 | Rail corrugation feature identification method based on wheel-rail noise wavelet packet decomposition |
| CN113501028A (en) * | 2021-07-07 | 2021-10-15 | 中国铁道科学研究院集团有限公司 | Method and device for diagnosing poor welded joint of heavy-duty railway steel rail |
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