CN110160778A - Gearbox fault state identification method based on sequential hypothesis testing - Google Patents
Gearbox fault state identification method based on sequential hypothesis testing Download PDFInfo
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses a kind of gearbox fault state identification method based on sequential hypothesis testing, this method are that identifying system using data available carries out self-adapting intelligent inquiry to propagation channel.Firstly, the pre-processing to extraction vibration signal using analysis method of wavelet packet.Secondly, extracting checked object of the kurtosis value sequence of vibration signal as sequential probability ratio test.Then according to sequential probability ratio test algorithm, effective recognition mode and gear crack degenerate case have been carried out to four kinds of states of gear-box.It finally combines sequential probability ratio test and root-mean-square error algorithm to carry out three sequences to gear-box vibration signal and passes through rate than examining.When solving the identification of fault detection multiple faults, recognition speed is slow, target identification inaccuracy and the low problem of recognition efficiency.
Description
Technical field
The invention belongs to technical field of nondestructive testing more particularly to a kind of gearbox fault shapes based on sequential hypothesis testing
State recognition methods.
Background technique
Gear-box is for transmitting power and changing the conventional machinery device of revolving speed, since it is with compact-sized, efficiency
Height, the characteristics such as service life length and the operation is stable, obtains extensive utilization in mechanical transmission fields.However, gear due to bearing for a long time
Carrying turns, and use condition is severe, it is easy to break down.Therefore, status monitoring and diagnosis are carried out to guarantee machinery to gear-box
Equipment normal operation has very important significance.The fault diagnosis of gear-box mainly includes gearbox fault infomation detection, spy
Sign is extracted and state recognition.Wherein, extract to the fault signature of gear-box is the key that realize fault diagnosis and difficult point.
Existing machinery fault diagnosis, because vibration signal is various, sampling heavy workload, and it is complicated, do not have and represents
Property.When carrying out multi-Fault State identification, it is difficult to distinguish fault category and position.And accuracy and real-time be fault detection most
Important capacity index.
Summary of the invention
The technical problem to be solved by the invention is to provide a kind of, and the gearbox fault state based on sequential hypothesis testing is known
Other method, when solving the identification of fault detection multiple faults, recognition speed is slow, target identification inaccuracy and recognition efficiency is low asks
Topic.
The technical solution adopted by the present invention to solve the technical problems is: providing a kind of gear based on sequential hypothesis testing
Case malfunction recognition methods, this approach includes the following steps, step 1, is believed using vibration of the analysis method of wavelet packet to extraction
It number is pre-processed；
Step 2, checked object of the kurtosis value sequence of vibration signal as sequential probability ratio test is extracted；
Step 3, according to sequential probability ratio test algorithm, pattern-recognition and fault detection are carried out to the state of gear-box；
Step 4, three sequences are carried out to gear-box vibration signal in conjunction with sequential probability ratio test and root-mean-square error algorithm to pass through
Rate is than examining.Due to noise, between gear engagement etc. interference so that extract vibration signal it is extremely complex, need to have signal
The pretreatment of effect.Wavelet package transforms have good noise reduction effect, and very careful decomposition and reconstruct, institute can be carried out to signal
To be pre-processed using wavelet package transforms to original vibration signal.
According to the above technical scheme, the step 1 specifically includes,
Step 21, WAVELET PACKET DECOMPOSITION is carried out to signal；
Step 22, optimal base is chosen；
Step 23, the selection and quantization of threshold value；
Step 24, wavelet package reconstruction is carried out to signal.
According to the above technical scheme, signal passes through j layers of WAVELET PACKET DECOMPOSITION, is obtained from low to high 2fA frequency band signals,
WAVELET PACKET DECOMPOSITION is expressed as follows:
Wherein, u (k) indicates that low-pass filter, v (k) indicate that high-pass filter, j indicate decomposed class；
Wavelet package reconstruction is as follows:
Wherein it is possible to select decomposed class j=3.Original vibration signal can have through three layers of WAVELET PACKET DECOMPOSITION and after reconstructing
The noise reduction of effect.This prepares the fault diagnosis of gear-box vibration signal for sequential probability ratio test.
Suitable wavelet packet functions are selected, signal is carried out using different filter equalizers at the signal of different frequency range
Wavelet reconstruction.Orthogonal wavelet transformation can only decomposed signal low frequency part, can not be used to decomposed signal high frequency at signal
The shortcomings that during reason, can carry out finer decomposition to the low frequency part and high frequency section of signal simultaneously to improve time-frequency
Resolution ratio.The advantages of wavelet package transforms, is to decompose the signal containing medium, high frequency information and will not generate careless omission and superfluous
It is remaining, part (detail section), so for the detailed information such as fine edge signal as main component, wavelet transformation cannot be right
It is effectively decomposed.Wavelet Packet Transform Method can overcome some limitations of wavelet transformation.
According to the characteristics of vibration signal and requirement of the sequential probability ratio test algorithm to signal, decomposed class j=3 is set,
Three layers of WAVELET PACKET DECOMPOSITION are carried out to original vibration signal.Original vibration signal is being obtained 8 just after three layers of WAVELET PACKET DECOMPOSITION
The signal of frequency band is handed over, analysis signal chooses optimal wavelet packet basis.Optimal characteristics after vibration signal is decomposed, in each frequency band
Information will highlight, and select suitable threshold value and its coefficient quantization is selected frequency band required for subsequent analysis.According to
Interference is rejected in processing of the above step to signal, chooses the wavelet package reconstruction that suitable frequency band carries out signal, obtains reconstruct letter
Number.
According to the above technical scheme, in the step 2, the kurtosis value sequence of vibration signal is extracted as sequential probability ratio test
Checked object, due to kurtosis value to impact vibrate it is very sensitive, so extract kurtosis value be used as to gear-box vibration signal
Carry out the characteristic value of sequential probability ratio test.
Assuming that one group of discrete signal XS=[x1, x2..., xN], wherein N=8192, kurtosis value can indicate are as follows:
Checked object of the kurtosis value sequence of vibration signal as sequential probability ratio test is extracted, since kurtosis value is to impact
Property vibration it is very sensitive, so extract kurtosis value be used as to gear-box vibration signal progress sequential probability ratio test characteristic value.
According to the above technical scheme, fault detection is carried out to the state of gear-box in the step 3 specifically,
Step 31: obtaining original vibration signal Si, Sj i, j=1...4, i ≠ j, carry out wavelet-packet noise reduction；
Step 32: formula (4) and (5) calculate kurtosis；
Step 33: the likelihood ratio parameter, Δ of sequential probability ratio test is calculated by formula (8)-(11)I, j, and judge ΔI, j
With the relationship of threshold value.Wherein according to sequential probability ratio test algorithm, mean value and standard deviation in inspection are defined as follows:
For four groups of vibration signals obtained in experiment, sequential probability ratio test model is constructed, is carried out according to inspection process
Fault identification.The likelihood ratio that vibration signal is calculated is denoted as Δ1,2(YS1), Δ1,2(YS2), Δ1,3(YS1), Δ1,3
(YS3), ΔIsosorbide-5-Nitrae(YS1), ΔIsosorbide-5-Nitrae(YS4).The model and likelihood ratio size of sequential probability ratio test and gear-box state recognition
Relationship will be analyzed in fault diagnosis result.
According to the above technical scheme, the step 32 specifically:
Assuming that the probability distribution of kurtosis value sequence meets null hypothesis H under one group of signal conditioningi: μ=μi, another group of signal strips
Kurtosis value sequence meets alternative hypothesis H under parti: μ=μi, standard deviation sigma is constant；When null hypothesis and alternative hypothesis are all set up, kurtosis
The joint probability density function of value sequence is calculated as Pik(yk) and Pjk(yk), it thus can calculate the likelihood ratio of sequential probability ratio test
λI, j(YSm), it is abbreviated as ΔI, j(YSm)；With reference to sequential probability ratio test algorithm, by ΔI, jIt is compared respectively with threshold value a, b, with
Determine gear-box status, wherein when null hypothesis and alternative hypothesis are all set up, the joint probability density letter of kurtosis value sequence
Number is defined as:
Wherein pik(yk) and pjk(yk) it is respectively probability density function under the conditions of null hypothesis and alternative hypothesis, therefore, sequence
Pass through the likelihood ratio of probability ratio test is defined as:
Wherein, pi0It is the prior probability under the conditions of null hypothesis, pj0It is the prior probability under the conditions of alternative hypothesis, λI, j(YSm)
Indicate the likelihood ratio of sequential probability ratio test；
It calculates for convenience in practical applications, the likelihood ratio formula (10) of sequential probability ratio test can simplify are as follows:
Wherein, parameter YSiAnd YSjRespectively indicate experiment vibration signal SiAnd SjKurtosis value sequence, parameter, ΔI, j(YSi) and
ΔI, j(YSj) respectively indicate kurtosis value sequence YSiAnd YSjLikelihood ratio.
Fault Diagnosis of Gear Case algorithm proposed by the present invention based on sequential probability ratio test is in addition to can be by normal gear
It is identified with failure gear, can also be used to identify various sizes of gear crack.
Sequential probability ratio test, obtained likelihood ratio are carried out to the vibration signal S2, S3, S4 that gear crack does not extract simultaneously
With the relationship of sequential test the number of iterations, sequential probability ratio test algorithm has carried out various sizes of gear crack signal effectively
Identification.Vibration signal S2, S3 is selected to construct sequential probability ratio test model, formula calculates likelihood ratio Δ2,3(YS2) and
Δ2,3(YS3).Compare likelihood ratio Δ2,3(YS2) and Δ2,3(YS3) with the result of threshold value a, b.
Likelihood ratio Δ2,3(YS2) it is less than threshold value b, illustrate that gear-box is in malfunction F2, i.e. gear crack is 25%；
Likelihood ratio Δ2,3(YS3) it is greater than threshold value a, illustrate that gear-box is in malfunction F3, as gear crack is 50%.
According to likelihood ratio Δ2,4(YS2)、Δ2,4(YS4) with the relationship of sequential test the number of iterations.Likelihood ratio Δ2,4(YS2) small
In threshold value b, illustrate that gear-box is malfunction F2, i.e. gear crack is 25%；Likelihood ratio Δ2,4(YS4) it is greater than threshold value a, explanation
Gear-box is malfunction F4, as 75% crackle.
Similarly, according to the likelihood ratio Δ of sequential probability ratio test3,4(YS3) and Δ3,4(YS4) sequential test the number of iterations
Relationship.Likelihood ratio Δ3,4(YS3) it is less than threshold value b, illustrate that gear-box is in malfunction F3, as 50% crackle.Likelihood ratio
Δ3,4(YS4) it is greater than threshold value a, illustrate that gear-box is malfunction F4, as 75% crackle.
It is all the result shows that the Fault Diagnosis of Gear Case algorithm based on sequential probability ratio test be it is effective, pass through analysis
Relationship between likelihood ratio and threshold value a, b can accurately gear-box vibration signal be identified.
According to the above technical scheme, step 3 middle gear box-like state fault detection is analyzed, is specifically included,
The mean μ of checking sequence0And μ1Difference, to the standard of likelihood ratio, the length of Check-Out Time and sequential probability ratio test
True rate influences；For assuming H0And H1, μ0And μ1Value determined by the vibration signal of gear-box；By threshold parameter a in inspection
1000 and -1000 are set as with b to identify likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) and determine gear-box state；For tooth
The fault diagnosis of roller box remembers prior probability Pi0And Pj0It is equal；Gear-box F1, F2, F3, F4Under the conditions of four groups of vibration signals extracting
S1, S2, S3, S4Mean value be denoted as μ respectively1, μ2, μ3, μ4, wherein F1For normal gear, F2, F3, F4For failure gear, and gear F2
Crack depth and width are respectivelyWithGear F3Crack depth and width areWithGear F4Crack depth and
Width isWithF2, F3, F4It is 0.4 for failure gear crack thickness；Formula (8)-(11) calculate sequential general
Rate than inspection likelihood ratio, by likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) identification gear-box is compared to threshold value respectively
State FiAnd Fj, by analyzing likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) relationship between threshold value a, b can be accurate respectively
Gear-box vibration signal is identified.
According to the above technical scheme, the step 4 specifically includes,
Step 41: after wavelet package transforms, formula calculates kurtosis value and obtains the vibration signal under gear-box various states
To kurtosis value sequence Y 'S；
Step 42: calculating likelihood ratio Δ with equation1,2(Y′S)、Δ1,3(Y′S)、ΔIsosorbide-5-Nitrae(Y′S) calculated simultaneously using formula
Root-mean-square error E1,2(Ys1)、E1,3(Ys1)、EIsosorbide-5-Nitrae(Ys1)；Work as E1, m(Ys1) < EC1, m=2, identification gear-box is normal when 3,4
State F1, otherwise, gear-box is malfunction F2、F3、F4One of them, wherein root-mean-square error is defined as follows:
Step 43: if E1, m(Ys1) > EC1, m=2, when 3,4, formula continues to calculate likelihood ratio Δ2,3(Y′S)、
Δ2,4(Y′S), then root-mean-square error E is calculated by equation2,3(Ys2) and E2,4(Ys2)；When meeting E2, m(Ys2) < EC1, m=3,4
When, identify malfunction F2, otherwise gear-box is malfunction F2、F3、F4One of them；
Step 44:E2, m(Ys2) < EC2, m=3,4, it continues with formula and calculates likelihood ratio Δ3,4(Y′S), then pass through equation
Calculate root-mean-square error E3,4(Ys3), if E3,4(Ys2) < EC3Identify the malfunction F of gear-box3, otherwise identify malfunction
F4。
According to the above technical scheme, for four kinds of state F1、F2、F3、F4Gear, choose every kind of state under 16 groups of vibrations
Signal, formula calculate separately the kurtosis value of this 64 groups of vibration signals, are denoted as Y 'Sm(M), m=1,2,3,4, M=1 ..., 16
(including 7169 sample datas in every group of kurtosis value sequence), kurtosis value sequence Y 'Sm(M) it is calculated as three layers of sequential probability ratio test
The inspection data of method；
According to inspection process, the likelihood ratio Δ of 64 groups of vibration signals is calculatedI, j(Y′Sm(M)), m=1,2,3,4, M=
1 ..., 16；For the same sequential probability ratio test model, i.e. i, when j is determined, 16 groups of vibration signals under a kind of state can
To obtain 16 likelihood ratios, the error between this 16 likelihood ratios is calculated with root-mean-square error algorithm, then calculate this 16 seemingly
So than the root-mean-square error between the likelihood ratio of vibration signal under other several states, finally, in conjunction with sequential probability ratio test
Algorithm and root-mean-square error algorithm identify the various states of gear-box.
According to the above technical scheme, in the step 4, according to the data obtained, recognition result is analyzed, verifies three sequences
Rate ratio is passed through to examine,
Firstly, the likelihood ratio Δ of applying vibration signal1,2(Y′S1)、Δ1,3(Y′S1)、ΔIsosorbide-5-Nitrae(Y′S1) identify gear-box
Normal condition F1；
Secondly, the likelihood ratio Δ of applying vibration signal2,3(Y′S2)、Δ2,4(Y′S2) identify gearbox fault state F2；
Finally, with the likelihood ratio Δ of sequential probability ratio test3,4(Y′S4) identify gearbox fault state F4。
The beneficial effect comprise that: original vibration signal is pre-processed using wavelet package transforms.Feature ginseng
Number can adequately reflect the characteristic information of signal, extract characteristic parameter with temporal analysis to pretreated signal, this
In extract very sensitive kurtosis value vibrated as characteristic value to impact, kurtosis value is gathered as sequential probability ratio test
Checking sequence.Fault diagnosis finally is carried out with vibration signal of the sequential probability ratio test algorithm to four kinds of state lower gears and is known
Not.Statistical nature is extracted using sequential probability ratio test, realizes the intelligent diagnostics to gear-box.Sequential probability ratio test is first
Data are observed according to the sample of extraction and establish statistic model, the basic assumption of check problem are reintroduced, finally, according to specific
Fault message is tested and is judged.The whole process of sequential probability ratio test detection efficiency with higher.In order to verify sequence
The diagnosis capability and feasibility for passing through probability ratio test algorithm, are mutually tied using root-mean-square error algorithm and sequential probability ratio test algorithm
The three layers of sequential probability ratio test closed calculate the error between failure of the same race and between failure not of the same race, present method solves
When fault detection multiple faults identifies, recognition speed is slow, target identification inaccuracy and the low problem of recognition efficiency.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is the flow diagram that the embodiment of the present invention is identified based on the gear-box multi-Fault State of sequential hypothesis testing；
Fig. 2 is in the embodiment of the present invention according to the fault identification of the sequential probability ratio test model testing vibration signal of building
Flow diagram；
Fig. 3 is the gear-box various faults state recognition process based on three layers of sequential probability ratio test in the embodiment of the present invention
Figure.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention.
In the embodiment of the present invention, a kind of gearbox fault state identification method based on sequential hypothesis testing, such as Fig. 1 are provided
It is shown, it mainly includes the following steps that, step S1: using analysis method of wavelet packet pre-processing to extraction vibration signal.
When specific implementation, suitable wavelet packet functions are selected, by signal using different filter equalizers at different frequency range
Signal, carry out wavelet reconstruction.Due to noise, the interference such as engagement is so that the vibration signal extracted from experiment is very multiple between gear
It is miscellaneous, it needs effectively to pre-process signal.Wavelet package transforms have good noise reduction effect, can carry out very to signal
Careful decomposition and reconstruct, so being pre-processed using wavelet package transforms to original vibration signal.
Step S2: checked object of the kurtosis value sequence of vibration signal as sequential probability ratio test is extracted.
When specific implementation, it is assumed that one group of discrete signal, wherein N=8192.Kurtosis value can indicate are as follows:
To gear-box vibration signal SiAll kurtosis values being calculated can be regarded as one group of checking sequence:
YSi=[y1...yk], i=1,2,3,4.
Step S3: according to sequential probability ratio test algorithm, effective recognition mode has been carried out to four kinds of states of gear-box
With gear crack degenerate case；
When specific implementation, the mean μ of checking sequence0And μ1Difference to likelihood ratio, the length of Check-Out Time, sequential probability
It is influenced than the accuracy rate of inspection very big.For assuming H0And H1, μ0And μ1Value determined by the vibration signal of gear-box.It is examining
It tests and middle set 1000 and -1000 for threshold parameter a and b and identify likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) and determine gear
The state of case.For the fault diagnosis of gear-box, prior probability P is countedi0And Pj0It is equal.Gear-box F1, F2, F3, F4Under the conditions of extract
Four groups of vibration signal S1, S2, S3, S4Mean value be denoted as μ respectively1, μ2, μ3, μ4.In summary it analyzes, is calculated with above formula
The likelihood ratio of sequential probability ratio test.By likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) identification tooth is compared to threshold value respectively
The state F of roller boxiAnd FjAll the result shows that the Fault Diagnosis of Gear Case algorithm based on sequential probability ratio test be it is effective,
By analyzing likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) relationship between threshold value a and b can accurately gear-box vibration respectively
Signal is identified.
Step S4: three sequences are carried out to gear-box vibration signal in conjunction with sequential probability ratio test and root-mean-square error algorithm and are passed through
Rate is than examining.
When specific implementation, comprising the following steps:
Step 41: after wavelet package transforms, formula calculates kurtosis value and obtains the vibration signal under gear-box various states
To kurtosis value sequence Y 'S
Step 42: calculating likelihood ratio Δ with equation1,2(Y′S)、Δ1,3(Y′S)、ΔIsosorbide-5-Nitrae(Y′S) calculated simultaneously using formula
Root-mean-square error E1,2(Ys1)、E1,3(Ys1)、EIsosorbide-5-Nitrae(Ys1).Work as E1, m(Ys1) < EC1, m=2, identification gear-box is normal when 3,4
State F1, otherwise, gear-box is malfunction F2、F3、F4One of them.
Step 43: if E1, m(Ys1) > EC1, m=2, when 3,4, formula continues to calculate likelihood ratio Δ2,3(Y′S)、
Δ2,4(Y′S), then root-mean-square error E is calculated by equation2,3(Ys2) and E2,4(Ys2).When meeting E2, m(Ys2) < EC1, m=3,4
When, identify malfunction F2, otherwise gear-box is malfunction.
Step 44:E2, m(Ys2) < EC2, m=3,4, it continues with formula and calculates likelihood ratio Δ3,4(Y′S), then pass through equation
Calculate root-mean-square error E3,4(Ys3).If E3,4(Ys2) < EC3Identify the malfunction F of gear-box3, otherwise identify malfunction
F4.Fig. 2 is the fault identification flow diagram of the sequential probability ratio test model testing vibration signal of the invention according to building,
Fig. 3 is the gear-box various faults state recognition flow chart of the invention based on three layers of sequential probability ratio test.
To sum up, the present invention illustrates utilization of the sequential probability ratio test algorithm in Gear Crack Faults identification, just
The vibration signal collected under four kinds of situations in experiment has carried out effective differentiation.Due to the original vibration signal folder acquired in experiment
Miscellaneous a large amount of noise, uses Wavelet Packet Transform Method to pre-process to achieve the effect that noise reduction signal here.Kurtosis value
It is that very sensitive time domain charactreristic parameter is vibrated to impact, the kurtosis value sequence for extracting vibration signal is examined as sequential probability ratio
The checked object tested.According to sequential probability ratio test algorithm, effective identification has been carried out to four kinds of states of gear-box.In order to test
The validity that sequential probability ratio test is applied to Gear Crack Faults identification is demonstrate,proved, in conjunction with sequential probability ratio test and root-mean-square error
Algorithm carries out three sequences to gear-box vibration signal and passes through rate than examining, and inspection result illustrates that sequential probability ratio test algorithm can be right
Gear Crack Faults are effectively identified.
The present invention, which is identifying system, carries out self-adapting intelligent inquiry to propagation channel using data available.Target identification is benefit
Mathematically estimate the shape size and weight of target.Identification process is exactly wherein true according to a large amount of training sample institutes in classification
Fixed function is identified.It is to depend on its most important spy that sequential probability ratio test, which is widely used in field of target recognition,
Point --- rapidity and high efficiency.When solving the identification of fault detection multiple faults, recognition speed is slow, target identification inaccuracy and knowledge
The problem of other low efficiency.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (10)
1. a kind of gearbox fault state identification method based on sequential hypothesis testing, which is characterized in that this method includes following
Step 1 step is pre-processed using vibration signal of the analysis method of wavelet packet to extraction；
Step 2, checked object of the kurtosis value sequence of vibration signal as sequential probability ratio test is extracted；
Step 3, according to sequential probability ratio test algorithm, pattern-recognition and fault detection are carried out to the state of gear-box；
Step 4, three sequences are carried out to gear-box vibration signal in conjunction with sequential probability ratio test and root-mean-square error algorithm and passes through rate ratio
It examines.
2. the gearbox fault state identification method according to claim 1 based on sequential hypothesis testing, which is characterized in that
The step 1 specifically includes,
Step 21, WAVELET PACKET DECOMPOSITION is carried out to signal；
Step 22, optimal base is chosen；
Step 23, the selection and quantization of threshold value；
Step 24, wavelet package reconstruction is carried out to signal.
3. the gearbox fault state identification method according to claim 2 based on sequential hypothesis testing, which is characterized in that
It specifically includes, signal passes through j layers of WAVELET PACKET DECOMPOSITION, is obtained from low to high 2fA frequency band signals, WAVELET PACKET DECOMPOSITION indicate
It is as follows:
Wherein, u (k) indicates that low-pass filter, v (k) indicate that high-pass filter, j indicate decomposed class；
Wavelet package reconstruction is as follows:
Wherein it is possible to select decomposed class j=3.
4. the gearbox fault state identification method according to claim 1 or 2 based on sequential hypothesis testing, feature exist
In, in the step 2,
Assuming that one group of discrete signal XS=[x1, x2..., xN], wherein N=8192, kurtosis value can indicate are as follows:
5. the gearbox fault state identification method according to claim 1 or 2 based on sequential hypothesis testing, feature exist
In, fault detection is carried out to the state of gear-box in the step 3 specifically,
Step 31: obtaining original vibration signal Si, sj, i, j=1...4, i ≠ j, carry out wavelet-packet noise reduction；
Step 32: formula (4) and (5) calculate kurtosis；
Step 33: the likelihood ratio parameter, Δ of sequential probability ratio test is calculated by formula (8)-(11)I, j, and judge ΔI, jWith threshold
The relationship of value.Wherein according to sequential probability ratio test algorithm, mean value and standard deviation in inspection are defined as follows:
6. the gearbox fault state identification method according to claim 5 based on sequential hypothesis testing, which is characterized in that
The step 32 specifically:
Assuming that the probability distribution of kurtosis value sequence meets null hypothesis H under one group of signal conditioningi: μ=μi, under another group of signal conditioning
Kurtosis value sequence meets alternative hypothesis Hi: μ=μi, standard deviation sigma is constant；When null hypothesis and alternative hypothesis are all set up, kurtosis value sequence
The joint probability density function of column is calculated as Pik(yk) and Pjk(yk), it thus can calculate the likelihood ratio λ of sequential probability ratio testI, j
(YSm), it is abbreviated as ΔI, j(YSm)；With reference to sequential probability ratio test algorithm, by ΔI, jIt is compared respectively with threshold value a, b, with true
Fixed tooth roller box status, wherein when null hypothesis and alternative hypothesis are all set up, the joint probability density function of kurtosis value sequence
Is defined as:
Wherein pik(yk) and pjk(yk) it is respectively probability density function under the conditions of null hypothesis and alternative hypothesis, it is therefore, sequential general
Likelihood ratio of the rate than inspection is defined as:
Wherein, pi0It is the prior probability under the conditions of null hypothesis, pj0It is the prior probability under the conditions of alternative hypothesis, λI, j(YSm) indicate
The likelihood ratio of sequential probability ratio test；
The likelihood ratio formula (10) of sequential probability ratio test can simplify are as follows:
Wherein, parameter YSiAnd YSjRespectively indicate the kurtosis value sequence of experiment vibration signal Si and Sj, parameter, ΔI, j(YSi) and ΔI, j
(YSj) respectively indicate kurtosis value sequence YSiAnd YSiLikelihood ratio.
7. the gearbox fault state identification method according to claim 6 based on sequential hypothesis testing, which is characterized in that
Step 3 middle gear box-like state fault detection is analyzed, is specifically included,
The mean μ of checking sequence0And μ1Difference, to the accuracy rate of likelihood ratio, the length of Check-Out Time and sequential probability ratio test
It influences；For assuming H0And H1, μ0And μ1Value determined by the vibration signal of gear-box；By threshold parameter a and b in inspection
1000 and -1000 are set as to identify likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) and determine gear-box state；For gear-box
Fault diagnosis, remember prior probability Pi0And Pj0It is equal；Gear-box F1, F2, F3, F4Under the conditions of four groups of vibration signal S extracting1,
S2, S3, S4Mean value be denoted as μ respectively1, μ2, μ3, μ4, wherein F1For normal gear, F2, F3, F4For failure gear, and gear F2It splits
Line depth and width are respectivelyWithGear F3Crack depth and width areWithGear F4Crack depth and width
Degree isWithF2, F3, F4It is 0.4 for failure gear crack thickness；Formula (8)-(11) calculate sequential probability
Than the likelihood ratio of inspection, by likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) shape of identification gear-box is compared to threshold value respectively
State FiAnd Fj, by analyzing likelihood ratio ΔI, j(YSi) and ΔI, j(YSj) relationship between threshold value a, b can be accurately right respectively
Gear-box vibration signal is identified.
8. the gearbox fault state identification method according to claim 1 or 2 based on sequential hypothesis testing, feature exist
In, the step 4 specifically includes,
Step 41: after wavelet package transforms, formula calculating kurtosis value obtains high and steep the vibration signal under gear-box various states
Angle value sequence Y 'S；
Step 42: calculating likelihood ratio Δ with equation1,2(Y′S)、Δ1,3(Y′S)、ΔIsosorbide-5-Nitrae(Y′S) square using formula calculating simultaneously
Root error E1,2(Ys1)、E1,3(Ys1)、EIsosorbide-5-Nitrae(Ys1)；Work as E1, m(Ts1) < EC1, m=2 identifies the normal condition of gear-box when 3,4
F1, otherwise, gear-box is malfunction F2、F3、F4One of them, wherein root-mean-square error is defined as follows:
Step 43: if E1, m(Ys1) > EC1, m=2, when 3,4, formula continues to calculate likelihood ratio Δ2,3(Y′S)、Δ2,4
(Y′S), then root-mean-square error E is calculated by equation2,3(Ys2) and E2,4(Ys2)；When meeting E2, m(Ts2) < EC1, m=3 when 4, knows
Other malfunction F2, otherwise gear-box is malfunction F2、F3、F4One of them；
Step 44:E2, m(Ys2) < EC2, m=3,4, it continues with formula and calculates likelihood ratio Δ3,4(Y′S), then calculated by equation
Root-mean-square error E3,4(Ys3), if E3,4(Ys2) < EC3Identify the malfunction F of gear-box3, otherwise identify malfunction F4。
9. the gearbox fault state identification method according to claim 8 based on sequential hypothesis testing, which is characterized in that
For four kinds of state F1、F2、F3、F4Gear, choose 16 groups of vibration signals under every kind of state, formula calculates separately this
The kurtosis value of 64 groups of vibration signals, is denoted as Y 'Sm(M), m=1,2,3,4, M=1 ..., 16, kurtosis value sequence Y 'Sm(M) conduct
The inspection data of three layers of sequential probability ratio test algorithm；
According to inspection process, the likelihood ratio Δ of 64 groups of vibration signals is calculatedI, j(Y′Sm(M)), m=1,2,3,4, M=1 ..., 16；
For the same sequential probability ratio test model, i.e. i, when j is determined, 16 groups of vibration signals available 16 under a kind of state
Likelihood ratio calculates the error between this 16 likelihood ratios with root-mean-square error algorithm, then calculates this 16 likelihood ratios and other
Root-mean-square error under several states between the likelihood ratio of vibration signal, finally, in conjunction with sequential probability ratio test algorithm and square
Root ERROR ALGORITHM identifies the various states of gear-box.
10. the gearbox fault state identification method according to claim 9 based on sequential hypothesis testing, feature exist
In, in the step 4, according to the data obtained, recognition result to be analyzed, three sequences of verifying pass through rate ratio inspection,
Firstly, the likelihood ratio Δ of applying vibration signal1,2(Y′S1)、Δ1,3(Y′S1)、ΔIsosorbide-5-Nitrae(Y′S1) identify the normal of gear-box
State F1；
Secondly, the likelihood ratio Δ of applying vibration signal2,3(Y′S2)、Δ2,4(Y′S2) identify gearbox fault state F2；
Finally, with the likelihood ratio Δ of sequential probability ratio test3,4(Y′S4) identify gearbox fault state F4。
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