CN102607845A - 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

Bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match

Technical field

The present invention relates to a kind of feature extracting method of rolling bearing, particularly a kind of bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match.

Background technology

Rolling bearing is one of component that the most often uses in the 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 possibly cause the serious consequence of casualties.Therefore, rolling bearing is carried out status monitoring, effectively extract the characteristic information that can reflect its running status, thereby find potential faults as early as possible, avoid the generation of accident, have crucial meaning.

The vibration signal of industry spot rolling bearing has the characteristics of non-stationary usually.For effectively catching the fault signature in the vibration signal, the wavelet transformation with good time frequency analysis ability has obtained using widely.Yet classical small echo needs to realize by convolution algorithm, causes calculated amount bigger; Simultaneously only also be difficult to mate the various complex characteristic in the vibration signal through a certain small echo.Though and Lifting Wavelet has solved two problems in the above-mentioned classical small echo, use the symmetrical wavelet of most often constructing at present based on interpolation formula, when extraction had the fault signature of asymmetry, still there was certain limitation in it.Therefore; Thought derivation according to approximation of function obtains the Lifting Wavelet building method based on data fitting; Thereby flexible construction goes out the small echo of a plurality of each tool characteristic comes vibration signal is carried out analyzing and processing; And set up objective function and come to choose adaptively the small echo that is matched with most fault signature, effectively extracting faint characteristic information, for the fault diagnosis of bearing provides foundation.

Summary of the invention

The objective of the invention is to: through a kind of bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match is provided; Extract the characteristic information that can reflect the bearing running status; To realize effective bearing state monitoring and fault diagnosis, assurance equipment is operation reposefully normally.

For realizing above-mentioned purpose, the present invention adopts technical scheme to realize:

A kind of bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match; Through vibration acceleration signal rolling bearing is carried out fault diagnosis; Application is constructed multiple wavelet function with different qualities based on the computing formula and the boosting algorithm of data fitting, and vibration acceleration signal is made the self-adaptive redundant lifting wavelet transform; Wherein, use computing formula and the multiple wavelet function of boosting algorithm structure, may further comprise the steps with different qualities based on data fitting:

1.1. confirm three different basis functions;

1.2. confirming three kinds, different (wherein, M is a sample points for M, N) value, and N is the dimension of basis function;

1.3. the predictive operator constructive formula according to based on the least square method of data fitting calculates the predictive operator coefficient, and gets that to upgrade operator length identical with predictive operator length, then the predictive operator coefficient can be obtained upgrading operator coefficient divided by two;

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

Wherein, vibration acceleration signal is made the self-adaptive redundant lifting wavelet transform, may further comprise the steps:

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

Successively signal x to be decomposed is made redundant lifting wavelet transform 2.2. use the multiple different small echos of being constructed, 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 normalization l respectively ^PNorm obtains a plurality of normalization l ^PNorm value.A plurality of numerical value are compared, get minimum low frequency approximation signal of norm value and high frequency detail signal and give up other results as the decomposition result of x;

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

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

At last, the signal that obtains through single reconstruct is made the Hilbert demodulation process, obtain the final envelope spectrogram of initial vibration acceleration signal; Frequency content in the spectrogram is extracted and discerned; Change frequently even its frequency multiplication composition if find to have, judge that then rolling bearing possibly break down; If find to have fault characteristic frequency even its frequency multiplication of outer ring or inner ring or rolling body or retainer, fault has taken place in then corresponding judgement outer ring or inner ring or rolling body or retainer.

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)}Cos (0.1 (k+1) x).

K=0 wherein, 1,2, Λ N, N are the dimension of basis function.

Aforesaid (M, value 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 remarkable advantages and beneficial effect:

1) through construction algorithm based on data fitting; Can construct Lifting Wavelet flexibly, easily with different qualities; Even can construct small echo with asymmetry; Compare the symmetrical wavelet that present application is constructed based on interpolation formula the most widely, can mate the fault signature that has asymmetry equally better.

2) signal is made the self-adaptive redundant lifting wavelet transform based on data fitting, can from nine kinds of different small echos of having constructed, choose the optimal wavelet that matees this signal characteristic most adaptively to each layer low frequency approximation signal to be decomposed on the one hand; On the other hand, guarantee that through redundant arithmetic the new low frequency approximation signal that obtains after each the decomposition still has identical sample points with the initial vibration signal with the high frequency detail 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) the initial vibration signal is made the segmented power analysis of spectrum, can under the situation of wavelet transformation, confirm to be used to do a certain low frequency approximation signal or the high frequency detail signal of single reconstruct exactly.

Description of drawings

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

Fig. 2 is based on the small echo construction process of data fitting and boosting algorithm;

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

Fig. 4 is based on the redundant lifting wavelet transform process of self-adaptation match.

Embodiment

Below in conjunction with accompanying drawing specific embodiment of the present invention is elaborated.

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

The bearing vibration signal that is collected by sensor and data acquisition unit is made the redundant lifting wavelet transform of self-adaptation match, obtain low frequency approximation signal and high frequency detail signal under each yardstick.

The initial vibration signal is made the segmented power analysis of spectrum.For sample points is the signal X of M, and its power spectrum is: to the amplitude of the Fourier transform F (X) of X squared after again divided by M.According to wavelet transformation promptly: at analysis frequency f to the frequency band division rule of signal _SDown, the low frequency approximation signal a that obtains after the decomposition of j layer _jWith high frequency detail signal d _jCorresponding frequency range be respectively [0, f _S/ 2 ^j] and [f _S/ 2 ^j, f _S/ 2 ^J-1].In view of the above 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 pairing 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 Hilbert demodulation and envelope spectrum analysis, extract relevant frequency content in the spectrogram.Change frequently even its frequency multiplication composition if find to have, judge that then rolling bearing possibly break down; If find to have fault characteristic frequency even its frequency multiplication of outer ring or inner ring or rolling body or retainer, fault has taken place in then corresponding judgement outer ring or inner ring or rolling body or retainer; If can't extract the said frequencies composition, then continue to gather the bearing vibration signal, and analyze once more according to above-mentioned four steps.

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

1) confirms basis function φ.Get three basis functions among the present invention altogether, be respectively: 1. algebraic expression φ _k(x)=x ^k2. 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)}Cos (0.1 (k+1) x).

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

3) constructive formula of using based on data fitting calculates the predictive operator coefficient.Make P represent predictive operator, L representes the length of predictive operator, and then 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) among length

the present invention of definite renewal operator, get

then upgrading operator coefficient is the half the of predictive operator coefficient.

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

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

As shown in Figure 4, the redundant lifting wavelet transform of self-adaptation match mainly contains following steps:

1) confirms the decomposition number of plies of wavelet transformation.Among the present invention, decompose the number of plies and be taken as three.Begin to carry out conversion, and make that the current decomposition number of plies is 1.Then the step of the redundant lifting wavelet transform of the self-adaptation match of one whole mainly contains:

1. with low frequency approximation signal a _jSignal x to be decomposed as each conversion.When j=0, be the initial vibration signal.

2. to current predictive operator FACTOR P _CurWith renewal operator coefficient U _CurCarry out the interpolation zero padding to realize redundant arithmetic.Promptly working as the predictive operator coefficient is P=[p ₁, p ₂, Λ p _L] time, the predictive operator coefficient after the 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 the interpolation zero padding.

3. with nine kinds of small echo ψ that the present invention constructed ₁～ψ ₉Successively to low frequency approximation signal a to be decomposed _j(being initial vibration signal x during j=0) made redundant lifting wavelet transform (predict and upgrade two steps), obtains 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, and expression is by small echo ψ ₁～ψ ₉Decompose the new signal that obtains).

4. to these nine groups of a _{J+1, k}And d _{J+1, k}Ask for normalization l respectively ^PNorm, computing formula is following:

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

${\left|\right|{\mathrm{<figure-callout\; id="1"\; label="b\; j\; +"\; filenames="HDA0000140645110000031.png"\; state="\{\{state\}\}">b</figure-callout>}}_{j+}\left|\right|}_P={\left(\underset{i}{\mathrm{\&Sigma;}}{|d_{i,j+1,k}/\underset{i}{\mathrm{\&Sigma;}}{d}_{i,j+1,k}|}^P\right)}^{1/P}$

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

Promptly ask for a respectively _{J+1, k}And d _{J+1, k}Norm, again both summations are obtained final norm value l ^P(a _{I, j, k}) _PIn the following formula, i=1,2, Λ M, expression 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) is got corresponding that group a of 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 a _{J+1, k}As the stylish signal x to be decomposed of conversion next time.Simultaneously, 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 characteristic.

2) after linear transformation finishes; Make the current decomposition number of plies add 1; 1. to 5. proceeding conversion next time, until reaching the initial decomposition number of plies of confirming (being taken as three among the present invention), the redundant lifting wavelet transform of then whole self-adaptation match finishes according to above-mentioned steps.

Claims (5)

1. bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match; Through vibration acceleration signal rolling bearing is carried out fault diagnosis; It is characterized in that: use computing formula and the multiple wavelet function of boosting algorithm structure, and vibration acceleration signal is made the self-adaptive redundant lifting wavelet transform with different qualities based on data fitting; Wherein, use computing formula and the multiple wavelet function of boosting algorithm structure, may further comprise the steps with different qualities based on data fitting:

1.1. confirm three different basis functions;

1.2. confirming three kinds, different (wherein, M is a sample points for M, N) value, and N is the dimension of basis function;

1.3. the predictive operator constructive formula according to based on the least square method of data fitting calculates the predictive operator coefficient, and gets that to upgrade operator length identical with predictive operator length, then the predictive operator coefficient can be obtained upgrading operator coefficient divided by two;

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

Wherein, vibration acceleration signal is made the self-adaptive redundant lifting wavelet transform, may further comprise the steps:

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

Successively signal x to be decomposed is made redundant lifting wavelet transform 2.2. use the multiple different small echos of being constructed, 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 normalization l respectively ^PNorm obtains a plurality of normalization l ^PNorm value.A plurality of numerical value are compared, get minimum low frequency approximation signal of norm value and high frequency detail signal and give up other results as the decomposition result of x;

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

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

At last, the signal that obtains through single reconstruct is made the Hilbert demodulation process, obtain the final envelope spectrogram of initial vibration acceleration signal; Frequency content in the spectrogram is extracted and discerned; Change frequently even its frequency multiplication composition if find to have, judge that then rolling bearing possibly break down; If find to have fault characteristic frequency even its frequency multiplication of outer ring or inner ring or rolling body or retainer, fault has taken place in then corresponding judgement outer ring or inner ring or rolling body or retainer.

2. the bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match according to claim 1, it is characterized in that: described multiple wavelet function with different qualities is nine kinds.

3. the bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match according to claim 1, it 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)}Cos (0.1 (k+1) x).

K=0 wherein, 1,2, Λ N, N are the dimension of basis function.

4. a kind of bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match according to claim 1 is characterized in that: described (M, value N) is respectively: (1) (4,3); (2) (6,5); (3) (8,7).

5. a kind of bearing fault feature extracting method based on the redundant lifting wavelet transform of self-adaptation match according to claim 1, it is characterized in that: the described decomposition number of plies is 3.

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