CN103439110B - Rolling bearing early-stage weak fault diagnostic method - Google Patents

Abstract

The object of the present invention is to provide rolling bearing early-stage weak fault diagnostic method, comprise the following steps: respectively acceleration transducer to be installed on the drive end and output terminal of pedestal, casing, gather each acceleration transducer vibration acceleration signal, obtain vibration acceleration signal z matrix; Adopt independent component analysis to carry out pre-service to vibration acceleration signal, realize the separation of vibration acceleration signal; Choose the separation signal comprising fault characteristic information; Adopt adaptive boosting morphological wavelet transformation to carry out fault-signal feature to the separation signal be selected accurately to extract; Make power spectrum chart by Pwelch method, observation power spectrum chart whether there is fault characteristic frequency or its frequency multiplication place exists obvious peak value, and then judges whether rolling bearing early-stage weak fault occurs.Not only the present invention has good details and retains and noiseproof feature, inhibits noise but also fully highlights the shock characteristic of fault-signal, have better early-stage weak fault feature extraction effect and counting yield.

Description

Rolling bearing early-stage weak fault diagnostic method

Technical field

What the present invention relates to is a kind of Fault Diagnosis of Roller Bearings, specifically faint in early days method for diagnosing faults.

Background technology

Rolling bearing is the critical component of rotating machinery, and its health status affects the duty of whole mechanical system, and the process not in time of chance failure will cause unthinkable consequence, is therefore of great significance the monitoring and diagnosis tool of bearing.Large-sized power is equipped, as aeromotor, genset etc., under the rugged surroundings such as high speed, heavy duty and thump, its core component bearing very easily damages, fault-signal early period of origination is very faint, and the vibration caused by other moving component and a large amount of random noise are flooded.Therefore, how from feeble signal or the signal that flooded by noise, extracting transient state Characteristics of Mutation, is carry out the key that initial failure accurately identifies.

Conventional fault-signal feature extracting method has temporal analysis and frequency domain analysis, wavelet transform filtering, lifting morphological wavelet, and these feature extracting methods also can analyze rolling bearing fault.But, also have some limitations when adopting these demodulation methods to analyze, traditional temporal analysis and frequency domain analysis analyze early-stage weak fault, but fault characteristic frequency may be flooded by the frequency structure information covering of other signal content and ground unrest, thus affect diagnostic result; Wavelet transform filtering, when decomposed signal, is often decomposed once, and the length of general picture signal reduces half, and along with the increase of decomposition scale, the information that general picture signal comprises is fewer and feweri, and temporal resolution reduces; Though promoting morphological wavelet is a kind of Nonlinear Wavelet Transform method based on mathematical morphology, not only remain morphologic nonlinear analysis characteristic, also there is the multi-resolution characteristics of wavelet decomposition, but promote morphological wavelet and be configured with a significantly restriction, namely filter operator is unalterable for the signal overall situation, and always there is certain sudden change in the signal, this just requires that sudden change place of signal has different filtering characteristics.

Summary of the invention

The object of the present invention is to provide the rolling bearing early-stage weak fault diagnostic method based on adaptive boosting morphological wavelet transformation.

The object of the present invention is achieved like this:

Rolling bearing early-stage weak fault diagnostic method of the present invention, is characterized in that:

(1) on the drive end and output terminal of pedestal, casing, respectively acceleration transducer is installed, gathers each acceleration transducer vibration acceleration signal, obtain vibration acceleration signal z matrix;

(2) adopt independent component analysis to carry out pre-service to vibration acceleration signal, realize the separation of vibration acceleration signal;

(3) separation signal comprising fault characteristic information is chosen;

(4) adopt adaptive boosting morphological wavelet transformation to carry out fault-signal feature to the separation signal be selected accurately to extract;

(5) make power spectrum chart by Pwelch method, observation power spectrum chart whether there is fault characteristic frequency or its frequency multiplication place exists obvious peak value, and then judges whether rolling bearing early-stage weak fault occurs.

The present invention can also comprise:

1, it is adopt to carry out decoupling zero separation based on the FastICA method of negentropy maximization to acceleration signal that described employing independent component analysis carries out pre-service to vibration acceleration signal:

(1) average and whitening processing are gone to vibration acceleration signal z matrix;

(2) by random weight vector w initialization, method of steepest descent is utilized to ask w ₀, initial iteration number of times k=0, choosing convergence decision content is critical;

(3) any one iteration point w is chosen _v, w _vimmobilize after choosing, by w _vand w ₀substitute into following formula: $w_{k+1}=E\left\{\mathrm{zg}\left(w_k^{T}z\right)\right\}{w}_v-E\left\{\mathrm{zg}\left(w_v^{T}z\right)\right\}{w}_k,$ Obtain w _k+1, in formula, g is non-quadratic function, E () for averaging, according to w _k+1=w _k+1/ ‖ w _k+1‖ normalization and decorrelation;

(4) judge | w _k+1-w _k| whether≤critical sets up, and is false then recoverable after k+1 $w_{k+1}=E\left\{\mathrm{zg}\left(w_k^{T}z\right)\right\}{w}_v-E\left\{\mathrm{zg}\left(w_v^{T}z\right)\right\}{w}_k,$ Continue iteration, if set up, algorithm convergence, estimates a separation matrix component;

(5) after obtaining whole separation matrix W, to be multiplied with vibration acceleration signal z by separation matrix W and to obtain the estimated signal of source signal, the then estimated signal x of output source signal.

2, the process choosing the separation signal comprising fault characteristic information is:

Selection principle is: peak factor C is defined as the ratio of peak value and root mean square, and its expression formula is: C=X _pEAK/ X _rMS, peak factor higher than 3.5 namely imply that fault.

3, adaptive boosting morphological wavelet transformation is adopted to carry out to the separation signal be selected the step that fault-signal feature accurately extracts:

L () carries out adaptive boosting morphological wavelet transformation to the separation signal be selected: select adaptive boosting morphological wavelet Decomposition order to be j, original signal is decomposed to jth layer, the wavelet details coefficient obtaining every layer is d ₁, d ₂... d _j,

Adaptive boosting morphological wavelet transformation implementation is:

$\left\{\begin{array}{c}{y}_{j+1}^{\text{'}}={\mathrm{\ω}}^{\↑}-P_c\left({\mathrm{\ψ}}^{\↑}\left(x_j\right)\right)\\ x_{j+1}^{\text{'}}={\mathrm{\ψ}}^{\↑}\left(x_j\right)-U_d[{\mathrm{\ω}}^{\↑}\left(x_j\right)-{\mathrm{\ψ}}^{\↑}\left(x_j\right)]\\ x_j={\mathrm{\ψ}}^{\↓}[x_{j+1}^{\text{'}}+U_d\left(y_{j+1}^{\text{'}}\right),y_{j+1}^{\text{'}}+P_c(x_{j+1}^{\text{'}}+U_d\left(y_{j+1}^{\text{'}}\right))]\end{array}\right.$

In formula: ω ^↑detail analysis operator, ψ ^↑signal analysis operator, ψ ^↓for the signal syntheses operator in Dual Wavelet decomposition, x _jfor original signal x being decomposed jth layer, x _jsplit into detail signal x' _j+1with general picture signal y' _j+1, then pass through x' _j+1and y' _j+1reconstruct x _j, P _cand U _dbe respectively the anticipation function and renewal function that are determined by C and D, C and D is respectively the determining function determining prediction and update operator, and determining function C and D of predictive operator and update operator is as follows

$C(x,y)=\left\{\begin{array}{c}-1|x\left(n\right)-y(n-1)|<|x\left(n\right)-y\left(n\right)|\\ +1|x\left(n\right)-y(n-1)|\&GreaterEqual;|x\left(n\right)-y\left(n\right)|\end{array}\right.$

$D(x,y)=\left\{\begin{array}{c}-1|x^{\text{'}}\left(n\right)-y^{\text{'}}(n-1)|<|x^{\text{'}}\left(n\right)-y^{\text{'}}\left(n\right)|\\ +1|x^{\text{'}}\left(n\right)-y^{\text{'}}(n-1)|\&GreaterEqual;|x^{\text{'}}\left(n\right)-y^{\text{'}}\left(n\right)|\end{array}\right.$

Anticipation function p _cwith renewal function U _dbe respectively

In formula: ∧ and ∨ is set indicative function;

(2) determining threshold values, processing decomposing the wavelet details coefficient obtained, obtaining the threshold coefficient after processing is

(3) the lifting morphological wavelet detail signal after threshold values process is carried out the reconstruct of lifting morphological wavelet, obtain the signal after noise reduction, thus accurately extract fault characteristic signals.

4, described convergence decision content critical=0.000001.

5, described threshold values is determined to be specially:

The adaptive threshold system of selection based on neighborhood relevance is adopted to process wavelet details coefficient, being configured to of threshold values function:

${\hat{d}}_{j,l}=d_{j,l}\&CenterDot;\{1-\exp [1-{\left(\frac{\left|S_{j,l}\right|}{{\mathrm{\&lambda;}}_j}\right)}^{\mathrm{\&alpha;}}\left]\right\}$

In formula: d _j,loriginal Lifting Wavelet coefficient, lifting Wavelet detail coefficients after threshold values process, α=4, λ _jfor the threshold values of jth decomposition layer, S _j,lbe centered by (j, l), size is the average of the operation neighborhood window of k=2l+1,

$S_{j,l}=\frac{1}{2k+1}\underset{i=-k}{\overset{k}{\mathrm{\&Sigma;}}}{d}_{j,l}(l+j).$

6, described determination threshold values is specially:

Threshold values λ _jthe function determined is:

${\mathrm{\&lambda;}}_j=\mathrm{\&beta;}\&CenterDot;\mathrm{\&sigma;}\sqrt{2\ln N}/\ln \left(j\right)$

In formula, 0< β≤1, N is the length of signal, and σ is noise criteria variance, and the following formula of σ is estimated

$\widehat{\mathrm{\&sigma;}}=\frac{\mathrm{median}\left(d\right)}{0.6745}$

In formula, d represents morphological wavelet detail coefficients, and median () represents median operator.

Advantage of the present invention is:

(1) due to mixing that vibration acceleration test signal is multiple vibration signal, cause the vibration signal relevant with fault often by structural vibration and interference noise pollute, particularly initial failure signal is often very faint, directly utilizes test signal to carry out fault diagnosis and is difficult to ensure Fault Identification ability.The present invention adopts independent component analysis to carry out pre-service to test signal, and structural vibration component and failure-frequency component are made a distinction, failure message is enhanced, for the efficient diagnosis of rolling bearing early-stage weak fault lays the foundation.

(2) adaptive boosting morphological wavelet transformation is a kind of Nonlinear wavelet analysis based on Mathematical Morphology, the analytical effect of traditional form small echo is not improved by means of only lifting scheme, and according to the adjustment prediction of the local feature information self-adapting of signal and update operator, the rolling bearing fault signal be more suitable for having non-stationary nonlinear characteristic processes.

(3) for overcoming the changeless shortcoming of lifting operator in conventional lift morphological wavelet, the basis of conventional lift morphological wavelet proposes a kind of adaptive boosting morphological wavelet building method, the method according to the lifting operator of the determination morphological wavelet of the consecutive point information self-adapting of detail signal and rough signal, can enhance the adaptivity promoting morphological wavelet analytic signal.

(4) the present invention adopts the adaptive threshold system of selection based on neighborhood relevance to process wavelet details signal, thus overcome the system of selection of Traditional Wavelet coefficient threshold only to the shortcoming that single wavelet coefficient processes, can the local feature information of better stick signal.

(5) the present invention is used for analyzing and monitoring rolling bearing early-stage weak fault, not only there is the multi-resolution characteristics of morphologic morphological character and small echo, and there is good details reservation and noiseproof feature, not only inhibit noise but also fully highlight the shock characteristic of fault-signal, have better early-stage weak fault feature extraction effect and counting yield, the efficient diagnosis for Weak fault provides certain technological means.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is early stage inner ring faulty bearing vibration acceleration test signal time domain beamformer;

Fig. 3 is the time domain plethysmographic signal figure of early stage inner ring faulty bearing vibration acceleration test signal after independent component analysis;

Fig. 4 is the time-domain diagram of the separation signal comprising failure message after adaptive boosting morphological wavelet is analyzed be selected;

Fig. 5 is the power spectrum chart of the separation signal comprising failure message after adaptive boosting morphological wavelet is analyzed be selected.

Embodiment

Below in conjunction with accompanying drawing citing, the present invention is described in more detail:

Composition graphs 1 ~ 5, the present invention includes the following step:

1) utilize acceleration transducer to carry out measurement to rolling bearing and obtain vibration acceleration test signal.Three passage vibration acceleration test signals of the present invention have the acceleration transducer be arranged on pedestal, the drive end of casing and output terminal to pick up respectively.

2) adopt independent component analysis to carry out pre-service to vibration acceleration test signal, realize the separation of signal of vibrating.The present invention adopts the FastICA method of improvement to carry out decoupling zero separation to vibration acceleration test signal, specifically comprises the following steps:

2.1) average and whitening processing are gone to vibration acceleration test signal z matrix;

2.2) by random weight vector w initialization, method of steepest descent is utilized to ask w ₀, initial iteration number of times k=0, choosing convergence decision content is critical=0.000001;

2.3) any one iteration point w is chosen _v, and w _vimmobilize after choosing, by w _vand w ₀substitution formula (1) obtains w _k+1, according to w _k+1=w _k+1/ ‖ w _k+1‖ normalization and decorrelation;

$w_{k+1}=E\left\{\mathrm{zg}\left(w_k^{T}z\right)\right\}{w}_v-E\left\{\mathrm{zg}\left(w_v^{T}z\right)\right\}{w}_k---\left(1\right)$

In formula: g is non-quadratic function, and E () is for averaging.

2.4) judge | w _k+1-w _k| whether≤critical sets up, and is false, and (1) formula that returns after k+1 continues iteration, sets up then algorithm convergence, estimates a separation matrix component;

2.5) after obtaining whole separation matrix W, to be multiplied with vibration acceleration test signal z by separation matrix W and to obtain the estimated signal of source signal, the then estimated signal x of output source signal.

3) separation signal comprising fault characteristic information is chosen.

Selection principle is: peak factor (C) is defined as peak value and the ratio of root mean square, represents whether waveform has the index of impact, and its expression formula is: C=X _pEAK/ X _rMS.Known theoretically, the peak factor of the vibration signal of normal bearing is approximately 2.5 ~ 3.5, namely imply that fault higher than the peak factor of 3.5.Because the value of crest is not by the impact of bearing size, rotating speed and load, so the size by calculating peak factor, can effectively to whether judging in signal containing failure message.

4) adopt adaptive boosting morphological wavelet transformation to carry out fault-signal feature to the separation signal be selected accurately to extract, specifically comprise the following steps:

4.l) adaptive boosting morphological wavelet transformation is carried out to the separation signal be selected.Select adaptive boosting morphological wavelet Decomposition order to be j, original signal is decomposed to jth layer, the wavelet details coefficient obtaining every layer is d ₁, d ₂... d _j.

Adaptive boosting morphological wavelet transformation implementation is:

$\left\{\begin{array}{c}{y}_{j+1}^{\text{'}}={\mathrm{\&omega;}}^{\&UpArrow;}-P_c\left({\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)\right)\\ x_{j+1}^{\text{'}}={\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)-U_d[{\mathrm{\&omega;}}^{\&UpArrow;}\left(x_j\right)-{\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)]\\ x_j={\mathrm{\&psi;}}^{\&DownArrow;}[x_{j+1}^{\text{'}}+U_d\left(y_{j+1}^{\text{'}}\right),y_{j+1}^{\text{'}}+P_c(x_{j+1}^{\text{'}}+U_d\left(y_{j+1}^{\text{'}}\right))]\end{array}\right.$

In formula: ω ^↑detail analysis operator, ψ ^↑signal analysis operator, ψ ^↓for the signal syntheses operator in Dual Wavelet decomposition, x _jfor original signal x being decomposed jth layer, x _jsplit into detail signal x' _j+1with general picture signal y' _j+1, then pass through x' _j+1and y' _j+1reconstruct x _j.P _cand U _dbe respectively the anticipation function and renewal function that are determined by C and D, C and D is respectively the determining function determining prediction and update operator.The present invention selects predictive operator and update operator according to the consecutive point information of detail signal and general picture signal.Determining function C and D of predictive operator and update operator is as follows

$C(x,y)=\left\{\begin{array}{c}-1|x\left(n\right)-y(n-1)|<|x\left(n\right)-y\left(n\right)|\\ +1|x\left(n\right)-y(n-1)|\&GreaterEqual;|x\left(n\right)-y\left(n\right)|\end{array}\right.$

$D(x,y)=\left\{\begin{array}{c}-1|x^{\text{'}}\left(n\right)-y^{\text{'}}(n-1)|<|x^{\text{'}}\left(n\right)-y^{\text{'}}\left(n\right)|\\ +1|x^{\text{'}}\left(n\right)-y^{\text{'}}(n-1)|\&GreaterEqual;|x^{\text{'}}\left(n\right)-y^{\text{'}}\left(n\right)|\end{array}\right.$

Anticipation function p _cwith renewal function U _dbe respectively

In formula: ∧ and ∨ is set indicative function.

4.2) select suitable threshold values disposal route to process decomposing the wavelet details coefficient obtained, obtaining the threshold coefficient after processing is

4.2.1. the adaptive threshold system of selection based on neighborhood relevance is adopted to process morphological wavelet detail signal, being configured to of threshold values function

${\hat{d}}_{j,l}=d_{j,l}\&CenterDot;\{1-\exp [1-{\left(\frac{\left|S_{j,l}\right|}{{\mathrm{\&lambda;}}_j}\right)}^{\mathrm{\&alpha;}}\left]\right\}$

In formula: d _j,loriginal Lifting Wavelet coefficient, be Lifting Wavelet detail coefficients after threshold values process, the present invention gets α=4, λ _jfor the threshold values of jth decomposition layer.S _j,lbe centered by (j, l), size is the average of the operation neighborhood window of k=2l+1.

$S_{j,l}=\frac{1}{2k+1}\underset{i=-k}{\overset{k}{\mathrm{\&Sigma;}}}{d}_{j,l}(l+j)$

4.2.2. the basis in conjunction with the system of selection of document threshold values proposes threshold values λ _jthe function determined is:

${\mathrm{\&lambda;}}_j=\mathrm{\&beta;}\&CenterDot;\mathrm{\&sigma;}\sqrt{2\ln N}/\ln \left(j\right)$

In formula, 0< β≤1, N is the length of signal, and σ is noise criteria variance, and σ can estimate with following formula

$\widehat{\mathrm{\&sigma;}}=\frac{\mathrm{median}\left(d\right)}{0.6745}$

In formula, d represents morphological wavelet detail coefficients, and median () represents median operator.

4.3) the lifting morphological wavelet detail signal after threshold values process is carried out the reconstruct of lifting morphological wavelet, obtain the signal after noise reduction, thus accurately extract fault characteristic signals.

5) make power spectrum chart by Pwelch method, and whether observations power spectrum chart exists fault characteristic frequency, and then judge whether rolling bearing early-stage weak fault occurs.

Accompanying drawing 2 is a time-domain diagram being provided with the SKF6205 type bearing vibration acceleration signal of early stage inner ring fault.Bear vibration acceleration signal test data comes from the bearing data center website of CaseWesternReserveUniversity.Three passage acceleration signals have the acceleration transducer be arranged on pedestal, the drive end of casing and output terminal to pick up respectively.The local damage of bearing is made in bearing inner race artificial by electric discharge machine, and diameter is 0.05334cm, and rotating speed is 1774r/min, and load is 0.735KW, and the characteristic frequency of inner ring fault is 159.7Hz.

Accompanying drawing 3 is the time domain plethysmographic signal figure of early stage inner ring faulty bearing test vibration acceleration signal after independent component analysis is separated.

Accompanying drawing 4 comprises the time-domain diagram of separation signal after adaptive boosting morphological wavelet analyzing and processing of fault characteristic information for the 3rd of being selected.The peak factor calculating three separation signals respectively obtains the C1=3.56 ≈ 3.5 of the 1st separation signal, the C2=3.39 < 3.5 of the 2nd separation signal, the C3=5.58 > 3.5 of the 3rd separation signal, so can judge that the 3rd separation signal comprises failure message, so carry out the analysis of adaptive boosting morphological wavelet to the 3rd separation signal, it effectively inhibits noise and background signal, and better highlights the impact composition characteristics of signal.

Accompanying drawing 5 is to the power spectrum chart of the separation signal 3 chosen after the analysis of adaptive boosting morphological wavelet.The frequency obtaining peak value larger from figure is about 29.7Hz, 130Hz, 159.7Hz, 360Hz, 390Hz, 449.7HZ respectively, therefrom finds, in power spectrum, has occurred with axle periodic structure frequently.Wherein 29.7Hz is turn frequency f of axle.Find that 130Hz, 360Hz, 390Hz, 449.7HZ are about the axle frequency multiplication of 5 times, 12 times, 13 times, 15 times frequently respectively, the modulation phenomenon that this illustrates is modulating frequency with the gyro frequency of axle simultaneously.In addition, the characteristic frequency 159.7Hz of early stage inner ring fault is also extracted accurately.And then can conclude, be that rolling bearing inner ring there occurs fault.Thus the validity demonstrated based on the rolling bearing early-stage weak fault diagnostic method of adaptive boosting morphological wavelet transformation and accuracy.

Claims (6)

1. rolling bearing early-stage weak fault diagnostic method, is characterized in that:

(1) on the drive end and output terminal of pedestal, casing, respectively acceleration transducer is installed, gathers each acceleration transducer vibration acceleration signal, obtain vibration acceleration signal z matrix;

(2) adopt independent component analysis to carry out pre-service to vibration acceleration signal, realize the separation of vibration acceleration signal;

(3) separation signal comprising fault characteristic information is chosen;

(4) adopt adaptive boosting morphological wavelet transformation to carry out fault-signal feature to the separation signal be selected accurately to extract;

(5) make power spectrum chart by Pwelch method, observation power spectrum chart whether there is fault characteristic frequency or its frequency multiplication place exists obvious peak value, and then judges whether rolling bearing early-stage weak fault occurs;

It is adopt to carry out decoupling zero separation based on the FastICA method of negentropy maximization to acceleration signal that described employing independent component analysis carries out pre-service to vibration acceleration signal:

(1) average and whitening processing are gone to vibration acceleration signal z matrix;

(2) by random weight vector w initialization, method of steepest descent is utilized to ask w ₀, initial iteration number of times k=0, choosing convergence decision content is critical;

(3) any one iteration point w is chosen _v, w _vimmobilize after choosing, by w _vand w ₀substitute into following formula: $w_{k+1}=E\left\{zg\left(w_k^{T}z\right)\right\}{w}_v-E\left\{zg\left(w_v^{T}z\right)\right\}{w}_k,$ Obtain w _k+1, in formula, g is non-quadratic function, E () for averaging, according to w _k+1=w _k+1/ || w _k+1|| normalization and decorrelation;

(4) judge | w _k+1-w _k| whether≤critical sets up, and is false then recoverable after k+1 $w_{k+1}=E\left\{zg\left(w_k^{T}z\right)\right\}{w}_v-E\left\{zg\left(w_v^{T}z\right)\right\}{w}_k,$ Continue iteration, if set up, algorithm convergence, estimates a separation matrix component;

(5) after obtaining whole separation matrix W, to be multiplied with vibration acceleration signal z by separation matrix W and to obtain the estimated signal of source signal, the then estimated signal x of output source signal.

2. rolling bearing early-stage weak fault diagnostic method according to claim 1, is characterized in that: the process choosing the separation signal comprising fault characteristic information is:

Selection principle is: peak factor C is defined as the ratio of peak value and root mean square, and its expression formula is: C=X _pEAK/ X _rMS, peak factor higher than 3.5 namely imply that fault.

3. rolling bearing early-stage weak fault diagnostic method according to claim 1, is characterized in that: adopt adaptive boosting morphological wavelet transformation to carry out to the separation signal be selected the step that fault-signal feature accurately extracts:

L () carries out adaptive boosting morphological wavelet transformation to the separation signal be selected: select adaptive boosting morphological wavelet Decomposition order to be j, original signal is decomposed to jth layer, the wavelet details coefficient obtaining every layer is d ₁, d ₂... d _j,

Adaptive boosting morphological wavelet transformation implementation is:

$\left\{\begin{array}{c}{y}_{j+1}^{\&prime;}={\mathrm{\&omega;}}^{\&UpArrow;}-P_c\left({\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)\right)\\ x_{j+1}^{\&prime;}={\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)-U_d\&lsqb;{\mathrm{\&omega;}}^{\&UpArrow;}\left(x_j\right)-{\mathrm{\&psi;}}^{\&UpArrow;}\left(x_j\right)\&rsqb;\\ x_j={\mathrm{\&psi;}}^{\&DownArrow;}\&lsqb;x_{j+1}^{\&prime;}+U_d\left(y_{j+1}^{\&prime;}\right),y_{j+1}^{\&prime;}+P_c\left(x_{j+1}^{\&prime;}+U_d\left(y_{j+1}^{\&prime;}\right)\right)\&rsqb;\end{array}\right.$

In formula: ω ^↑detail analysis operator, ψ ^↑signal analysis operator, ψ ^↓for the signal syntheses operator in Dual Wavelet decomposition, x _jfor original signal x being decomposed jth layer, x _jsplit into detail signal x' _j+1with general picture signal y' _j+1, then pass through x' _j+1and y' _j+1reconstruct x _j, P _cand U _dbe respectively the anticipation function and renewal function that are determined by C and D, C and D is respectively the determining function determining prediction and update operator, and determining function C and D of predictive operator and update operator is as follows

$C(x,y)=\left\{\begin{array}{c}-1\left|x\right(n)-y(n-1\left)\right|<\left|x\right(n)-y(n\left)\right|\\ +1\left|x\right(n)-y(n-1\left)\right|\&GreaterEqual;\left|x\right(n)-y(n\left)\right|\end{array}\right.$

$D(x,y)=\left\{\begin{array}{c}-1\left|x^{\&prime;}\right(n)-y^{\&prime;}(n-1\left)\right|<\left|x^{\&prime;}\right(n)-y^{\&prime;}(n\left)\right|\\ +1\left|x^{\&prime;}\right(n)-y^{\&prime;}(n-1\left)\right|\&GreaterEqual;\left|x^{\&prime;}\right(n)-y^{\&prime;}(n\left)\right|\end{array}\right.$

Anticipation function p _cwith renewal function U _dbe respectively

In formula: with for set indicative function;

(2) determining threshold values, processing decomposing the wavelet details coefficient obtained, obtaining the threshold coefficient after processing is

(3) the lifting morphological wavelet detail signal after threshold values process is carried out the reconstruct of lifting morphological wavelet, obtain the signal after noise reduction, thus accurately extract fault characteristic signals.

4. rolling bearing early-stage weak fault diagnostic method according to claim 1, is characterized in that: described convergence decision content critical=0.000001.

5. rolling bearing early-stage weak fault diagnostic method according to claim 3, is characterized in that: described threshold values is determined to be specially:

The adaptive threshold system of selection based on neighborhood relevance is adopted to process wavelet details coefficient, being configured to of threshold values function:

${\hat{d}}_{j,l}=d_{j,l}\&CenterDot;\left\{1-\exp \&lsqb;1-{\left(\frac{\left|S_{j,l}\right|}{{\mathrm{\&lambda;}}_j}\right)}^{\mathrm{\&alpha;}}\&rsqb;\right\}$

In formula: d _j,loriginal Lifting Wavelet coefficient, lifting Wavelet detail coefficients after threshold values process, α=4, λ _jfor the threshold values of jth decomposition layer, S _j,lbe centered by (j, l), size is the average of the operation neighborhood window of k=2l+1,

$S_{j,l}=\frac{1}{2k+1}\underset{i=-k}{\overset{k}{\&Sigma;}}{d}_{j,l}(l+j).$

6. rolling bearing early-stage weak fault diagnostic method according to claim 3, is characterized in that: described determination threshold values is specially:

Threshold values λ _jthe function determined is:

${\mathrm{\&lambda;}}_j=\mathrm{\&beta;}\&CenterDot;\mathrm{\&sigma;}\sqrt{2\ln N}/ln\left(j\right)$

In formula, 0 < β≤1, N is the length of signal, and σ is noise criteria variance, and the following formula of σ is estimated

$\widehat{\mathrm{\&sigma;}}=\frac{median\left(d\right)}{0.6745}$

In formula, d represents morphological wavelet detail coefficients, and median () represents median operator.