CN102607845B - Bearing fault characteristic extracting method for redundantly lifting wavelet transform based on self-adaptive fitting - Google Patents

Abstract

The invention provides a bearing fault characteristic extracting method for lifting wavelet transform based on self-adaptive fitting. The bearing fault characteristic extracting method is used for diagnosing faults of a rolling bearing through a vibration acceleration signal, and comprises the following steps of: creating nine wavelets with different characteristics through calculation formulas and lifting algorithms based on data fitting; carrying out redundant lifting wavelet transform on a vibration signal by using the nine created wavelets in sequence; determining the optimum and abandoning the other eight in nine groups of decomposition results according to a normalized 1P norm value; analyzing segmented power spectrums of the initial vibration acceleration signal; selecting the optimum low-frequency approximation signal or a high-frequency detail signal for single reconstruction; subjecting the signal obtained by the single reconstruction to Hilbert demodulation; and judging running state of the rolling bearing according to frequency components in an enveloping spectrum. According to invention, early weak fault characteristic information of the rolling bearing can be extracted more effectively, and evidences are provided for state monitoring and fault diagnosis of the rolling bearing, so that accidents can be avoided as possible.

Description

Based on the bearing fault characteristics extracting method of auto-adapted fitting Redundant Lifting wavelet transformation

Technical field

The present invention relates to a kind of feature extracting method of rolling bearing, particularly a kind of bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation.

Background technology

Rolling bearing is one of component the most often using in modern production equipment, because of caused faults of reason such as its normal running wastage and misoperations, not only can cause great economic loss to enterprise, even may cause the serious consequence of casualties.Therefore, rolling bearing is carried out to status monitoring, effectively extract the characteristic information that can reflect its running status, thereby find as early as possible potential faults, avoid the generation of accident, tool is of great significance.

The vibration signal of industry spot rolling bearing has the feature of non-stationary conventionally.For effectively catching the fault signature in vibration signal, the wavelet transformation with good time frequency analysis ability is widely used.But classical small echo need be realized by convolution algorithm, cause calculated amount larger; Only also be difficult to mate the various complex characteristic in vibration signal by a certain small echo simultaneously.And although Lifting Wavelet has solved two problems in above-mentioned classical small echo, the most often symmetrical wavelet based on interpolation formula structure of application at present, in the time that extraction has the fault signature of asymmetry, it still has some limitations.Therefore, derive and obtain the Construction Method for Lifting Wavelet Transform based on data fitting according to the thought of approximation of function, thereby flexible construction goes out the small echo of multiple each tool characteristics carries out analyzing and processing to vibration signal, and set up objective function and choose adaptively the small echo that is matched with most fault signature, effectively to extract faint characteristic information, for the fault diagnosis of bearing provides foundation.

Summary of the invention

The object of the invention is to: by a kind of bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation is provided, extract the characteristic information that can reflect bearing running status, to realize effective bearing condition monitoring and fault diagnosis, guarantee equipment is operation reposefully normally.

For achieving the above object, the present invention adopts technical scheme to realize:

A kind of bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation, by vibration acceleration signal, rolling bearing is carried out to fault diagnosis, computing formula and the boosting algorithm structure multiple wavelet function with different qualities of application based on data fitting, and vibration acceleration signal is made to self-adaptive redundant lifting wavelet transform; Wherein, computing formula and the boosting algorithm structure multiple wavelet function with different qualities of application based on data fitting, comprises the following steps:

1.1. determine three different basis functions;

1.2. determine three kinds of different (M, N) values, wherein, M is sample points, the dimension that N is basis function;

1.3. calculate predictive operator coefficient according to the predictive operator constructive formula of the least square method based on data fitting, and it is identical with predictive operator length to get renewal operator length, predictive operator coefficient can be obtained upgrading operator coefficient divided by two;

1.4. according to the relation between the predictive operator of gained, renewal operator and wavelet filter, construct corresponding Lifting Wavelet;

Wherein, vibration acceleration signal is made to self-adaptive redundant lifting wavelet transform, comprises the following steps:

2.1. current predictive operator coefficient and renewal operator coefficient are carried out to interpolation zero padding, realize redundant arithmetic;

2.2. the multiple different small echos that application is constructed are made Redundant Lifting wavelet transformation to signal x to be decomposed successively, obtain newly-generated low frequency approximation signal and the high frequency detail signal of many groups;

2.3. above-mentioned low frequency approximation signal and high frequency detail signal are got respectively to normalization l ^pnorm, obtains multiple normalization l ^pnorm value.Multiple numerical value is compared, get the low frequency approximation signal of norm value minimum and high frequency detail signal as the decomposition result of x and give up other results;

Determine and decompose number of plies j; All carry out according to 2.1,2.2,2.3 step each decomposition; Through the self-adaptive redundant lifting wavelet transform of j layer, will obtain j low frequency approximation signal and j high frequency detail signal;

Again, initial vibration acceleration signal is made to segmented power analysis of spectrum, get the corresponding low frequency approximation signal of prominent frequency range or high frequency detail signal and carry out single reconstruct;

Finally, the signal obtaining through single reconstruct is made to Hilbert demodulation process, obtain the final envelope spectrogram of initial vibration acceleration signal; Frequency content in spectrogram is extracted and identified; Turn even its frequency multiplication composition of frequency if find that there is, judge that rolling bearing may break down; If find that there is even its frequency multiplication of fault characteristic frequency of outer ring or inner ring or rolling body or retainer, there is fault in corresponding judgement outer ring or inner ring or rolling body or retainer.

The aforesaid multiple wavelet function with different qualities is nine kinds.

Aforesaid basis function φ is respectively:

(1) algebraic expression φ _k(x)=x ^k;

(2) override type φ _k(x)=x ^k0.6 ^{(0.1 (k+1) x)};

(3) override type φ _k(x)=x ^k2 ^{(0.1 (k+1) x)}(0.1 (k+1) x) for cos.

Wherein k=0,1,2, Λ N, the dimension that N is basis function.

The value of aforesaid (M, N) is respectively: (1) (4,3); (2) (6,5); (3) (8,7).

The aforesaid decomposition number of plies is 3.

The present invention compared with prior art, has following obvious advantage and beneficial effect:

1) by the construction algorithm based on data fitting, can construct flexibly, easily the Lifting Wavelet with different qualities, even can construct the small echo with asymmetry, compare the symmetrical wavelet of constructing based on interpolation formula being most widely used at present, can mate better the fault signature equally with asymmetry.

2) signal is made to the self-adaptive redundant lifting wavelet transform based on data fitting, can from nine kinds of different small echos of having constructed, choose adaptively the optimal wavelet that mates most this signal characteristic to every one deck low frequency approximation signal to be decomposed on the one hand; On the other hand, ensure that by redundant arithmetic the new low frequency approximation signal and the high frequency detail signal that after each decomposition, obtain still have identical sample points with initial vibration signal, thereby contain the more information of horn of plenty.By above-mentioned both, finally more effectively to extract the feature information of weak faults of rolling bearing.

3) initial vibration signal is made to segmented power analysis of spectrum, can be the in the situation that of wavelet transformation, be identified for exactly doing a certain low frequency approximation signal or the high frequency detail signal of single reconstruct.

Brief description of the drawings

Fig. 1 is overview flow chart of the present invention;

Fig. 2 is the Construction of Wavelets process based on data fitting and boosting algorithm;

Fig. 3 is nine kinds of different small echos of constructing based on data fitting constructive formula and boosting algorithm;

Fig. 4 is based on auto-adapted fitting Redundant Lifting wavelet transformation process.

Embodiment

Below in conjunction with accompanying drawing, specific embodiments of the invention are elaborated.

As shown in Figure 1, the holistic approach process of vibration acceleration signal mainly contains four steps:

The bearing vibration signal being collected by sensor and data acquisition unit is made to auto-adapted fitting Redundant Lifting wavelet transformation, obtain low frequency approximation signal and high frequency detail signal under each yardstick.

Initial vibration signal is made to segmented power analysis of spectrum.The signal X that is M for sample points, its power spectrum is: after the amplitude of the Fourier transform F (X) to X is squared again divided by M.According to wavelet transformation to the frequency band division rule of signal: at analysis frequency f _sunder, the low frequency approximation signal a that j layer obtains after decomposing _jwith high frequency detail signal d _jcorresponding frequency range is respectively [0, f _s/ 2 ^j] and [f _s/ 2 ^j, f _s/ 2 ^j-1].Accordingly to the frequency spectrum of initial vibration signal according to a _jand d _jthe power in each frequency range is divided and asked for to corresponding frequency range, thereby obtain the segmented power spectrum of initial vibration signal.

Each segmented power is compared, get the corresponding a of prominent frequency range _jor d _jdo single reconstruct, also realize " filtering " function of wavelet transformation simultaneously.

The signal of single reconstruct is done to Hilbert demodulation and envelope spectrum analysis, extract relevant frequency content in spectrogram.Turn even its frequency multiplication composition of frequency if find that there is, judge that rolling bearing may break down; If find that there is even its frequency multiplication of fault characteristic frequency of outer ring or inner ring or rolling body or retainer, there is fault in corresponding judgement outer ring or inner ring or rolling body or retainer; If cannot extract said frequencies composition, continue to gather the vibration signal of bearing, and again analyze according to above-mentioned four steps.

As shown in Figure 2, the construction process of the Lifting Wavelet based on data fitting mainly contains five steps:

1) determine basis function φ.In the present invention, get altogether three basis functions, be respectively: 1. algebraic expression φ _k(x)=x ^k; 2. override type φ _k(x)=x ^k0.6 ^{(0.1 (k+1) x)}; 3. override type φ _k(x)=x ^k2 ^{(0.1 (k+1) x)}(0.1 (k+1) x) for cos.

2) determine the combination (M, N) of sample points M and basis function dimension N.In the present invention, get altogether three kinds of sample points, be respectively 4,6 and 8; Get altogether three kinds of basis function dimensions, be respectively 3,5 and 7; And obtain altogether three kinds (M, N), be respectively (4,3), (6,5) and (8,7).

3) constructive formula of application based on data fitting calculates predictive operator coefficient.Make P represent predictive operator, L represents the length of predictive operator, and constructive formula is:

$P_L={\left[\begin{array}{c}{\mathrm{\φ}}_0\left(\frac{1+M}{2}\right)\\ {\mathrm{\φ}}_1\left(\frac{1+M}{2}\right)\\ M\\ {\mathrm{\φ}}_N\left(\frac{1+M}{2}\right)\end{array}\right]}^T{\left[\begin{array}{cccc}({\mathrm{\φ}}_0,{\mathrm{\φ}}_0)& ({\mathrm{\φ}}_0,{\mathrm{\φ}}_1)& \mathrm{\Λ}& ({\mathrm{\φ}}_0,{\mathrm{\φ}}_N)\\ ({\mathrm{\φ}}_1,{\mathrm{\φ}}_0)& ({\mathrm{\φ}}_1,{\mathrm{\φ}}_1)& \mathrm{\Λ}& ({\mathrm{\φ}}_1,{\mathrm{\φ}}_N)\\ M& M& K& M\\ ({\mathrm{\φ}}_N,{\mathrm{\φ}}_0)& ({\mathrm{\φ}}_N,{\mathrm{\φ}}_1)& \mathrm{\Λ}& ({\mathrm{\φ}}_N,{\mathrm{\φ}}_N)\end{array}\right]}^{-1}\left[\begin{array}{cccc}{\mathrm{\φ}}_0\left(x_1\right)& {\mathrm{\φ}}_0\left(x_2\right)& \mathrm{\Λ}& {\mathrm{\φ}}_0\left(x_M\right)\\ {\mathrm{\φ}}_1\left(x_1\right)& {\mathrm{\φ}}_1\left(x_2\right)& \mathrm{\Λ}& {\mathrm{\φ}}_1\left(x_M\right)\\ M& M& \mathrm{\Λ}& M\\ {\mathrm{\φ}}_N\left(x_1\right)& {\mathrm{\φ}}_N\left(x_2\right)& \mathrm{\Λ}& {\mathrm{\φ}}_N\left(x_M\right)\end{array}\right]$

4) determine the length of upgrading operator in the present invention, get upgrade the half that operator coefficient is predictive operator coefficient.

5) according to the relation between predictive operator, renewal operator and wavelet decomposition, reconfigurable filter, structure obtains new small echo.

As shown in Figure 3, for construct the nine kinds of small echos of the present invention that obtain according to Fig. 2 step: in figure, 1., 2. and 3. the numeral of wavelet shapes figure top distinguishes step 1 in presentation graphs 2) selected three basis functions; Presentation graphs 2 steps 2 are distinguished in (4,3), (6,5) and (8,7) in wavelet shapes figure left side) in selected three kinds (M, N).

As shown in Figure 4, auto-adapted fitting Redundant Lifting wavelet transformation mainly contains following steps:

1) determine the decomposition number of plies of wavelet transformation.In the present invention, decompose the number of plies and be taken as three.Start to convert, and to make the current decomposition number of plies be 1.Once the step of complete auto-adapted fitting Redundant Lifting wavelet transformation mainly contains:

1. with low frequency approximation signal a _jas the signal x to be decomposed of each conversion.In the time of j=0, be initial vibration signal.

2. to current predictive operator FACTOR P _curwith renewal operator coefficient U _curcarry out interpolation zero padding to realize redundant arithmetic.When predictive operator coefficient is P=[p ₁, p ₂, Λ p _l] time, the predictive operator coefficient after interpolation zero padding is P _red=[p ₁, 0, p ₂, 0, Λ 0, p _l], in like manner can obtain the renewal operator coefficient after interpolation zero padding.

3. nine kinds of small echo ψ that the present invention constructed ₁～ψ ₉successively to low frequency approximation signal a to be decomposed _j(when j=0, be initial vibration signal and x) make Redundant Lifting wavelet transformation (predict and upgrade two steps), obtain nine groups of newly-generated low frequency approximation signal a _{j+1, k}with high frequency detail signal d _{j+1, k}(k=1,2, Λ 9 represent by small echo ψ ₁～ψ ₉decompose the new signal obtaining).

4. to these nine groups of a _{j+1, k}and d _{j+1, k}ask for respectively normalization l ^pnorm, computing formula is as follows:

${\left|\right|a_{j+1,k}\left|\right|}_P={\left(\underset{i}{\mathrm{\Σ}}{|a_{i,j+1,k}/\underset{i}{\mathrm{\Σ}}{a}_{i,j+1,k}|}^P\right)}^{1/P}$

${\left|\right|b_{j+1,k}\left|\right|}_P={\left(\underset{i}{\mathrm{\Σ}}{|d_{i,j+1,k}/\underset{i}{\mathrm{\Σ}}{d}_{i,j+1,k}|}^P\right)}^{1/P}$

l ^P(a _i，j，k)＝||a _j+1，k|| _P+||d _j+1，k|| _P

Ask for respectively a _{j+1, k}and d _{j+1, k}norm, then both summations are obtained to final norm value l ^p(a _{i, j, k}) _p.In above formula, i=1,2, Λ M, represents a _{j+1, k}or d _{j+1, k}in i coefficient.

5. compare nine norm value l ^p(a _{i, j, k}) _pthe size of (k=1,2, Λ 9), gets that group a corresponding to minimum value _{j+1, k}and d _{j+1, k}as final decomposition result and give up other eight groups of results, and with this _{j+1, k}as convert stylish signal x to be decomposed next time.Meanwhile, get to decompose and obtain this and organize final a _{j+1, k}and d _{j+1, k}small echo as being matched with most a _jthe optimal wavelet of feature.

2) after linear transformation finishes, make the current decomposition number of plies add 1, according to above-mentioned steps, 1. to 5. proceed to convert next time, until reach initial definite decomposition number of plies (being taken as three in the present invention), whole auto-adapted fitting Redundant Lifting wavelet transformation carries out complete.

Claims (5)

1. the bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation, by vibration acceleration signal, rolling bearing is carried out to fault diagnosis, it is characterized in that: computing formula and the boosting algorithm structure multiple wavelet function with different qualities of application based on data fitting, and vibration acceleration signal is made to self-adaptive redundant lifting wavelet transform; Wherein, computing formula and the boosting algorithm structure multiple wavelet function with different qualities of application based on data fitting, comprises the following steps:

1.1. determine three different basis functions;

1.2. determine three kinds of different (M, N) values, wherein, M is sample points, the dimension that N is basis function;

1.3. calculate predictive operator coefficient according to the predictive operator constructive formula of the least square method based on data fitting, and it is identical with predictive operator length to get renewal operator length, predictive operator coefficient can be obtained upgrading operator coefficient divided by two;

1.4. according to the relation between the predictive operator of gained, renewal operator and wavelet filter, construct corresponding Lifting Wavelet;

Wherein, vibration acceleration signal is made to self-adaptive redundant lifting wavelet transform, comprises the following steps:

2.1. current predictive operator coefficient and renewal operator coefficient are carried out to interpolation zero padding, realize redundant arithmetic;

2.2. the multiple different small echos that application is constructed are made Redundant Lifting wavelet transformation to signal x to be decomposed successively, obtain newly-generated low frequency approximation signal and the high frequency detail signal of many groups;

2.3. above-mentioned low frequency approximation signal and high frequency detail signal are got respectively to normalization l ^pnorm, obtains multiple normalization l ^pnorm value; Multiple numerical value is compared, get the low frequency approximation signal of norm value minimum and high frequency detail signal as the decomposition result of x and give up other results;

Determine and decompose number of plies j; All carry out according to 2.1,2.2,2.3 step each decomposition; Through the self-adaptive redundant lifting wavelet transform of j layer, will obtain j low frequency approximation signal and j high frequency detail signal;

Again, initial vibration acceleration signal is made to segmented power analysis of spectrum, get the corresponding low frequency approximation signal of prominent frequency range or high frequency detail signal and carry out single reconstruct;

Finally, the signal obtaining through single reconstruct is made to Hilbert demodulation process, obtain the final envelope spectrogram of initial vibration acceleration signal; Frequency content in spectrogram is extracted and identified; Turn even its frequency multiplication composition of frequency if find that there is, judge that rolling bearing may break down; If find that there is even its frequency multiplication of fault characteristic frequency of outer ring or inner ring or rolling body or retainer, there is fault in corresponding judgement outer ring or inner ring or rolling body or retainer.

2. the bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation according to claim 1, is characterized in that: the described multiple wavelet function with different qualities is nine kinds.

3. the bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation according to claim 1, is characterized in that: described basis function φ is respectively:

(1) algebraic expression φ _k(x)=x ^k;

(2) override type φ _k(x)=x ^k0.6 ^{(0.1 (k+1) x)};

(3) override type φ _k(x)=x ^k2 ^{(0.1 (k+1) x)}(0.1 (k+1) x) for cos;

Wherein k=0,1,2 ... N, the dimension that N is basis function.

4. a kind of bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation according to claim 1, is characterized in that: the value of described (M, N) is respectively: (1) (4,3); (2) (6,5); (3) (8,7).

5. a kind of bearing fault characteristics extracting method based on auto-adapted fitting Redundant Lifting wavelet transformation according to claim 1, is characterized in that: the described decomposition number of plies is 3.