CN107621367A - A kind of rolling bearing damage degree assessment method - Google Patents

A kind of rolling bearing damage degree assessment method Download PDF

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CN107621367A
CN107621367A CN201710718344.XA CN201710718344A CN107621367A CN 107621367 A CN107621367 A CN 107621367A CN 201710718344 A CN201710718344 A CN 201710718344A CN 107621367 A CN107621367 A CN 107621367A
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CN107621367B (en
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蒋章雷
吴雅朋
徐小力
左云波
吴国新
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Beijing Information Science and Technology University
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Abstract

The present invention relates to a kind of rolling bearing damage degree assessment method based on diagonal slice spectrum and grey relational grade, its step：Using existing rotor testbed analog machine running status, the vibration signal of rotor testbed is gathered；All vibration signals are carried out with three-order cumulant spectrum operation, obtains the spectrogram under normal signal and different faults degree；Three-order cumulant data are done with grey relational grade analysis, obtains the lesion diameter grey relational grade curve map of bearing fault-signal early stage；The unknown failure vibration signal of physical device is gathered, abovementioned steps processing is carried out to vibration signal, corresponding diagonal slice spectrum is produced, obtains bearing fault frequency, failure judgement position；Vibration signal dimensionless index and the normal signal grey correlation angle value of physical device unknown failure are calculated, is depicted in damage of the bearing diameter and degree of association matched curve figure, according to position of the degree of association on curve, judges the size of damage of the bearing diameter.

Description

A kind of rolling bearing damage degree assessment method
Technical field
The present invention relates to a kind of rotary mechanical part damage degree assessment method, and diagonal slices are based on especially with regard to one kind The rolling bearing damage degree assessment method of spectrum and grey relational grade.
Background technology
Rolling bearing is most widely used a kind of load-carrying unit in rotating machinery, and whether its running status is normal often The performance of whole plant equipment is directly affected, and rolling bearing is also one of failure element occurred frequently in plant equipment.Work as bearing There is local damage or during defect, it is situations such as often making equipment produce much noise and abnormal vibration, heavy then damage equipment Bring inestimable consequence.
The content of the invention
In view of the above-mentioned problems, it is an object of the invention to provide a kind of axis of rolling based on diagonal slice spectrum and grey relational grade Damage degree assessment method is held, this method can effectively suppress Gauss and random noise, suppress non-frequency coupling composition and meter The small characteristic of calculation amount, obtains clearly failure-frequency information.
To achieve the above object, the present invention takes following technical scheme：One kind is based on diagonal slice spectrum and grey relational grade Rolling bearing damage degree assessment method, it is characterised in that comprise the following steps：(1) set using existing rotor testbed simulation Standby running status, gather the vibration signal xi of rotor testbedw={ x1,...xN, wherein, i representing fault types, i=1 is represented Normal bearing vibration signal, i=2,3,4 represent three kinds of different lesion diameters of bearing respectively；N represents every group of data amount check；W generations Table data group number, w=1 ..., 9；(2) to all vibration signal xiwThree-order cumulant spectrum operation is carried out, is obtained just Spectrogram under regular signal and different faults degree；Grey relational grade analysis is done to three-order cumulant data, obtained The lesion diameter of bearing fault-signal early stage-grey relational grade curve map；(3) the unknown failure vibration letter of physical device is gathered Number, the processing of step (2) is carried out to vibration signal, obtains corresponding diagonal slice spectrum, and then bearing fault frequency is obtained, judge Abort situation；The vibration signal dimensionless index and normal signal grey correlation angle value of physical device unknown failure are calculated, by it It is depicted in damage of the bearing diameter and degree of association matched curve figure, according to position of the degree of association on curve, judges damage of the bearing The size of diameter.
Further, in the step 2), detailed process is as follows：(a) by all vibration signal xiw={ x1,...xNIn N Individual data are divided into K sections, every section of M data, per segment data as a record；(b) averaging operation is carried out to each record； (c) setIt is j-th of record, j-th is recorded and seeks its Third-order cumulants, j=1 ... K；H=0,1 ... M-1； (d) it is the maximum delay amount of estimation to make l=k=τ, τ, obtains three-order cumulant(e) each group of three ranks are taken The average three-order cumulant estimate Ci as each group observations of cumulant diagonal slicesw(τ)；(f) to three Rank cumulant diagonal slices estimate Ciw(τ) does Fourier transformation, obtains all vibration signal xiwDiagonal slice spectrum Siw (ω)；(g) three-order cumulant estimate Ci is calculatedwThe kurtosis index Ci of (τ)q, margin index CLifWith pulse index Cif；(h) normal bearing vibration signal dimensionless index is set as reference sequence x1, the bearing fault letter compared with reference sequence Number dimensionless index is compares ordered series of numbers x2, x3, x4；Contrast ordered series of numbers and the degree of association R of reference sequence is calculatedi；(i) according to pass Connection degree Ri, damage of the bearing diameter and association are depicted in as abscissa using the degree of association as ordinate, failure lesion diameter Spend in X-Y scheme, obtain damage of the bearing diameter and degree of association matched curve.
Further, in the step (c), j-th of record seeks its Third-order cumulants：
In formula, M1=max (0 ,-l ,-k)；M2=min (M-1, M-1-l, M-1-k)；When l represents second-order cumulant maximum Prolong；K represents Third-order cumulants maximum delay.
Further, in the step (d), three-order cumulant
Further, in the step (e), three-order cumulant estimate Ciw(τ) is：
Further, in the step (f), diagonal slice spectrum Siw(ω) is：
In formula, ω represents frequency.
Further, in the step (g), kurtosis index Ciq, margin index CLifWith pulse index CifRespectively：
In formula, Ciw(τ)p=max (Ciw(τ))；
Further, in the step (h), ordered series of numbers x is contrastediWith reference sequence x1Degree of association RiComputational methods are as follows：If ginseng Examine ordered series of numbers x1(k)=[C1q,CL1f,C1f], compare ordered series of numbers x2(k), x3(k), x4(k) it is respectively：
x2(k)=[C2q,CL2f,C2f],
x3(k)=[C3q,CL3f,C3f],
x4(k)=[C4q,CL4f,C4f]；
Calculate each group and compare ordered series of numbers and the incidence coefficient δ of reference sequencei(k), according to incidence coefficient δi(k) contrast is calculated Ordered series of numbers xiFor reference sequence x1Degree of association RiFor：
Further, the incidence coefficient δi(k) it is：
In formula, ε is resolution ratio, and value is between 0-1；M=3, n=3, i=2,3,4；γ(x1(k),xi(k)) represent x1And x (k)i(k) incidence coefficient between.
For the present invention due to taking above technical scheme, it has advantages below：1st, the present invention can effectively suppress Gauss and Random noise, suppress non-frequency coupling composition and the small characteristic of amount of calculation, obtain clearly failure-frequency information.2nd, it is of the invention Combined using with grey relational grade, obtain the lesion diameter and degree of association curve map of bearing fault, bearing damage can be obtained with this Hinder the size of diameter.3rd, the present invention is established on the basis of experimental data, and algorithm is composed to bearing using three-order cumulant Vibration signal carries out spectrum analysis, it can be determined that bearing fault position, dimensionless ginseng is done to three-order cumulant data The grey relational grade analysis of number index, obtains bearing lesion diameter early stage, and theoretical ginseng is provided for the operational maintenance of equipment, maintenance Examine.
Brief description of the drawings
Fig. 1 is damage of the bearing diameter-grey relational grade curve map of the present invention.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of rolling bearing damage degree assessment method based on diagonal slice spectrum and grey relational grade, should Method comprises the following steps that：
(1) using existing rotor testbed analog machine normal operating condition, collection rotor testbed is in normal operation shape Vibration signal xi under statew={ x1,...xN, wherein, i=1 represents normal bearing vibration signal；N represents every group of data amount check； W represents data group number, w=1 ..., and 9；Using three kinds of fault degrees of experimental bench analog machine failure, three kinds of fault degrees are designated as Bearing inner race (or outer ring) lesion diameter 0.1778mm, 0.3556mm, 0.5334mm, collection rotor testbed is under three kinds of failures Vibration signal, be designated as xiw={ x1,...xN, wherein, N represents every group of data amount check；W represents data group number, w=1 ..., and 9； I representing fault types, i=2,3,4；Three kinds of different lesion diameters of bearing inner race (or outer ring) are represented respectively, such as 0.1778mm, 0.3556mm, 0.5334mm.
(2) to all vibration signal xiwThree-order cumulant spectrum operation is carried out, obtains normal signal and different event Spectrogram under barrier degree；Three-order cumulant data are done with grey relational grade analysis, obtains bearing failure early stage letter Number lesion diameter-grey relational grade curve map.
Comprise the following steps that：
(a) by all vibration signal xiw={ x1,...xNIn N number of data be divided into K sections, every section of M data, per hop count According to as a record.
(b) averaging operation is carried out to each record.
(c) setBe j-th record (j=1 ... K；H=0,1 ... M-1), j-th of record is asked thirdly rank Cumulant：
In formula, M1=max (0 ,-l ,-k)；M2=min (M-1, M-1-l, M-1-k)；When l represents second-order cumulant maximum Prolong；K represents Third-order cumulants maximum delay.
(d) l=k=τ (τ is the maximum delay amount of estimation) are made, obtain three-order cumulant：
(e) the average Third-order cumulants cutting on the cross as each group observations of each group of three-order cumulant is taken Piece estimate Ciw(τ)：
(f) to Ciw(τ) does Fourier transformation, obtains CiwDiagonal slice spectrum Si corresponding to (τ)w(ω)：
In formula, ω represents frequency.
(g) three-order cumulant estimate Ci is calculatedwThe kurtosis index Ci of (τ)q, margin index CLifAnd pulse Index Cif：
In formula, Ciw(τ)p=max (| Ciw(τ)|)；
(h) normal bearing vibration signal dimensionless index is set as reference sequence：
x1(k)=[C1q,CL1f,C1f]；
Bearing fault signal dimensionless index compared with reference sequence is to compare ordered series of numbers x2(k), x3(k), x4(k)：
x2(k)=[C2q,CL2f,C2f],
x3(k)=[C3q,CL3f,C3f],
x4(k)=[C4q,CL4f,C4f]；
Calculate each group and compare ordered series of numbers (fault-signal dimensionless index) and reference sequence (normal signal dimensionless index) Incidence coefficient δi(k)：
In formula, ε is resolution ratio, and value typically takes 0.5 between 0-1；M=3, n=3, i=2,3,4；γ(x1(k), xi(k) x) is represented1And x (k)i(k) incidence coefficient between.
According to incidence coefficient δi(k) contrast ordered series of numbers x is calculatediWith reference sequence x1Degree of association Ri：
(i) according to the pass for comparing ordered series of numbers (fault-signal dimensionless index) and reference sequence (normal signal dimensionless index) Connection degree Ri, damage of the bearing diameter and association are depicted in as abscissa using the degree of association as ordinate, failure lesion diameter Spend in X-Y scheme, obtain damage of the bearing diameter and degree of association matched curve, as shown in Figure 1.
(3) the unknown failure vibration signal of physical device is gathered, the processing of step (2) is carried out to vibration signal, is obtained pair The diagonal slice spectrum answered, and then bearing fault frequency is obtained, failure judgement position；Calculate the vibration letter of physical device unknown failure Number dimensionless index (comparing ordered series of numbers) and normal signal (reference sequence) grey correlation angle value, are depicted in damage of the bearing diameter In degree of association matched curve figure, according to position of the degree of association on curve, the size of damage of the bearing diameter is judged.
For example, finding the ordinate position of grey correlation angle value on Fig. 1 curves, the vertical seat through grey correlation angle value is done Cursor position horizontal linear, lesion diameter-grey relational grade intersections of complex curve abscissa is found, as hold the size of lesion diameter.When When lesion diameter is less than 0.1mm, do not break down；When lesion diameter in 0.1mm between 0.2mm, minor failure；Work as damage Diameter in 0.2mm between 0.4mm, moderate failure；When lesion diameter is more than 0.4mm, severe failure.
The various embodiments described above are merely to illustrate the present invention, and structure and size, set location and the shape of each part are all can be with It is varied from, on the basis of technical solution of the present invention, all improvement carried out according to the principle of the invention to individual part and waits With conversion, should not exclude outside protection scope of the present invention.

Claims (9)

  1. A kind of 1. rolling bearing damage degree assessment method based on diagonal slice spectrum and grey relational grade, it is characterised in that including Following steps：
    (1) using having rotor testbed analog machine running status, the vibration signal xi of rotor testbed is gatheredw={ x1, ...xN, wherein, i representing fault types, i=1 represents normal bearing vibration signal, and i=2,3,4 represent three kinds of bearing not respectively Same lesion diameter；N represents every group of data amount check；W represents data group number, w=1 ..., and 9；
    (2) to all vibration signal xiwThree-order cumulant spectrum operation is carried out, obtains normal signal and different faults journey Spectrogram under degree；Three-order cumulant data are done with grey relational grade analysis, obtains bearing fault-signal early stage Lesion diameter-grey relational grade curve map；
    (3) the unknown failure vibration signal of physical device is gathered, the processing of step (2) is carried out to vibration signal, is obtained corresponding Diagonal slice spectrum, and then bearing fault frequency is obtained, failure judgement position；Calculate physical device unknown failure vibration signal without Dimension index and normal signal grey correlation angle value, are depicted in damage of the bearing diameter and degree of association matched curve figure, root According to position of the degree of association on curve, the size of damage of the bearing diameter is judged.
  2. A kind of 2. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 1 Method, it is characterised in that：In the step 2), detailed process is as follows：
    (a) by all vibration signal xiw={ x1,...xNIn N number of data be divided into K sections, every section of M data, make per segment data For a record；
    (b) averaging operation is carried out to each record；
    (c) setIt is j-th of record, j-th is recorded and seeks its Third-order cumulants, j=1 ... K；H=0,1 ... M- 1；
    (d) it is the maximum delay amount of estimation to make l=k=τ, τ, obtains three-order cumulant
    (e) the average three-order cumulant as each group observations of each group of three-order cumulant is taken to estimate Evaluation Ciw(τ)；
    (f) to three-order cumulant estimate Ciw(τ) does Fourier transformation, obtains all vibration signal xiwIt is diagonal Section spectrum Siw(ω)；
    (g) three-order cumulant estimate Ci is calculatedwThe kurtosis index Ci of (τ)q, margin index CLifWith pulse index Cif；
    (h) normal bearing vibration signal dimensionless index is set as reference sequence x1, the bearing fault letter compared with reference sequence Number dimensionless index is compares ordered series of numbers x2, x3, x4；Contrast ordered series of numbers and the degree of association R of reference sequence is calculatedi；
    (i) according to degree of association Ri, bearing damage is depicted in as abscissa using the degree of association as ordinate, failure lesion diameter Hinder in diameter and degree of association X-Y scheme, obtain damage of the bearing diameter and degree of association matched curve.
  3. A kind of 3. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 2 Method, it is characterised in that：In the step (c), j-th of record seeks its Third-order cumulants：
    <mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>M</mi> <mn>1</mn> </msub> </mrow> <mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> </msubsup> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo>+</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo>+</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> </mrow>
    In formula, M1=max (0 ,-l ,-k)；M2=min (M-1, M-1-l, M-1-k)；L represents second-order cumulant maximum delay；K tables Show Third-order cumulants maximum delay.
  4. A kind of 4. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 3 Method, it is characterised in that：In the step (d), three-order cumulant
    <mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>M</mi> <mn>1</mn> </msub> </mrow> <mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> </msubsup> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>h</mi> <mo>+</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>h</mi> <mo>+</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  5. A kind of 5. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 2 Method, it is characterised in that：In the step (e), three-order cumulant estimate Ciw(τ) is：
    <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>K</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </msubsup> <msubsup> <mi>xi</mi> <mi>w</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  6. A kind of 6. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 2 Method, it is characterised in that：In the step (f), diagonal slice spectrum Siw(ω) is：
    <mrow> <msub> <mi>Si</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>&amp;tau;</mi> <mo>=</mo> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mi>&amp;omega;</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
    In formula, ω represents frequency.
  7. A kind of 7. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 2 Method, it is characterised in that：In the step (g), kurtosis index Ciq, margin index CLifWith pulse index CifRespectively：
    <mrow> <msub> <mi>Ci</mi> <mi>q</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>9</mn> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>w</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>9</mn> </msubsup> <mfrac> <mrow> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <mi>&amp;Sigma;</mi> <msup> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>|</mo> <mo>-</mo> <mover> <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <msubsup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow>
    <mrow> <msub> <mi>CLi</mi> <mi>f</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>9</mn> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>w</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>9</mn> </msubsup> <mfrac> <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>p</mi> </msub> </mrow> <mrow> <mo>|</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <mi>&amp;Sigma;</mi> <msqrt> <mrow> <mo>|</mo> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </msqrt> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow>
    <mrow> <msub> <mi>Ci</mi> <mi>f</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>9</mn> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>w</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>9</mn> </msubsup> <mfrac> <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>p</mi> </msub> </mrow> <mrow> <mo>|</mo> <mover> <mrow> <msub> <mi>Ci</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow>
    In formula, Ciw(τ)p=max (| Ciw(τ)|)；
  8. A kind of 8. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 2 Method, it is characterised in that：In the step (h), ordered series of numbers x is contrastediWith reference sequence x1Degree of association RiComputational methods are as follows：
    If reference sequence x1(k)=[C1q,CL1f,C1f], compare ordered series of numbers x2(k), x3(k), x4(k) it is respectively：
    x2(k)=[C2q,CL2f,C2f],
    x3(k)=[C3q,CL3f,C3f],
    x4(k)=[C4q,CL4f,C4f]；
    Calculate each group and compare ordered series of numbers and the incidence coefficient δ of reference sequencei(k), according to incidence coefficient δi(k) contrast ordered series of numbers is calculated xiFor reference sequence x1Degree of association RiFor：
    <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msub> <mi>&amp;delta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  9. A kind of 9. rolling bearing damage scale evaluation side based on diagonal slice spectrum and grey relational grade as claimed in claim 8 Method, it is characterised in that：The incidence coefficient δi(k) it is：
    <mrow> <msub> <mi>&amp;delta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munder> <mi>min</mi> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <mi>m</mi> </mrow> </munder> <munder> <mi>min</mi> <mrow> <mi>k</mi> <mo>&amp;Element;</mo> <mi>n</mi> </mrow> </munder> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>&amp;CenterDot;</mo> <munder> <mi>max</mi> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <mi>m</mi> </mrow> </munder> <munder> <mi>max</mi> <mrow> <mi>k</mi> <mo>&amp;Element;</mo> <mi>n</mi> </mrow> </munder> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>&amp;CenterDot;</mo> <munder> <mi>max</mi> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <mi>m</mi> </mrow> </munder> <munder> <mi>max</mi> <mrow> <mi>k</mi> <mo>&amp;Element;</mo> <mi>n</mi> </mrow> </munder> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mfrac> </mrow>
    In formula, ε is resolution ratio, and value is between 0-1；M=3, n=3, i=2,3,4；γ(x1(k),xi(k) x) is represented1(k) With xi(k) incidence coefficient between.
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