CN107562979A - A kind of rolling bearing performance degradation assessment method based on FOA WSVDD - Google Patents
A kind of rolling bearing performance degradation assessment method based on FOA WSVDD Download PDFInfo
- Publication number
- CN107562979A CN107562979A CN201710559685.7A CN201710559685A CN107562979A CN 107562979 A CN107562979 A CN 107562979A CN 201710559685 A CN201710559685 A CN 201710559685A CN 107562979 A CN107562979 A CN 107562979A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- munderover
- msup
- mfrac
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a kind of rolling bearing performance degradation assessment method based on FOA WSVDD, it is characterized in that：The time domain of bear vibration data and the characteristic vector of time-frequency domain are first extracted, and feature selecting is carried out based on monotonicity；Then performance degradation assessment model is established using normal condition characteristic vector；For gaussian kernel function to the insensitive problem of initial failure, Wavelet Kernel Function is incorporated into SVDD algorithms；Difficult problem is selected for SVDD algorithm parameters, using the ratio of supporting vector number and total number of samples as fitness function, its nuclear parameter is optimized using improved FOA, establishes FOA WSVDD assessment models.The evaluation index of last calculation bearing Life cycle vibration data, the performance degradation situation of bearing is assessed with this.Compared to the SVDD performance degradation assessment models established based on gaussian kernel function, it is more sensitive to bearing initial failure based on FOA WSVDD rolling bearing performance degradation assessment model, monotonicity between fault degree is more preferable, has accurately reflected the health status of bearing.
Description
Technical field
The invention belongs to bearing performance degradation assessment technical field, and in particular to one kind is based on FOA-WSVDD (Fruit
Fly Optimization Algorithm-Wavelet support vector data description) rolling bearing
Performance degradation assessment method.
Background technology
As industry and the continuous improvement of scientific and technological level, plant equipment are constantly changed complicated, efficient, light-duty etc.
Enter, while also face harsher working environment.Once the critical component of equipment breaks down, it is possible to can influence whole life
Production process, huge economic loss is caused, the problems such as resulting even in casualties.Therefore, maintenance of equipment is just by traditional thing
Maintenance and planned maintenance change to the condition maintenarnce based on state afterwards, and as the premise for establishing rational maintenance strategy, equipment
Energy degradation assessment also begins to receive much concern.
Rolling bearing directly affects whole and set as one of key components and parts in rotating machinery, the quality of its performance state
Standby operational reliability.In general, rolling bearing can all undergo from normally to degeneration up to the mistake to fail in use
Journey, and a series of different performance degradation states are generally undergone during this.If the mistake that can be degenerated in rolling bearing performance
The degree that bearing performance is degenerated is monitored in journey, then can is targetedly organized to produce and formulate rational maintenance meter
Draw, the generation for preventing unit exception from failing.
At present, the assessment for rolling bearing running status can be divided into：Characteristic index method and assessment models method.Feature refers to
Mark method includes：Time domain index, frequency-domain index, time-frequency index.Characteristic index method can reflect the operation of bearing to a certain extent
Stability indicator (such as root-mean-square value, root amplitude) in state, such as time domain index can gradually increase with fault progression
Greatly, but the position of initial damage can not be judged.And sensitiveness index (such as kurtosis index) though the position of initial damage can be identified,
But as the trend fallen after rising can be presented in the development of failure, and the development trend of bearing fault degree is not met.Assessment models
Method be exactly it is comprehensive choose various features index, using intelligence learning algorithm, performance degradation assessment model is established, so as to which obtain can
Comprehensively reflect the characteristic index of rolling bearing performance degenerative process.Conventional intelligence learning algorithm has logistic regression
(logistic regression, LR), Support Vector data description (support vector data description,
SVDD) etc..For LR algorithm, it is necessary to establish model using the data under different faults pattern in application process, limit it should
Use scope.SVDD algorithms only need the data modeling of a small amount of normal condition, have higher precision and stronger Shandong in the application
Rod, the shortcomings that overcoming LR algorithm, it is widely used.But when data have multi-modal distribution, its precision can be by
To very big influence, and the local message of signal can not be reflected.
The content of the invention
The present invention proposes that one kind is based on FOA-WSVDD to more timely and accurately reflect the early stage degenerate state of bearing
Rolling bearing performance degradation assessment method.
To achieve these goals, the present invention is achieved through the following technical solutions：
Step (1)：The vibration data under bearing normal condition is obtained, denoising is carried out and normalization pre-processes；Extraction vibration
The time domain of data, time and frequency domain characteristics vector, and feature selecting is carried out based on monotonicity；
Step (2)：By the optimizing spatial spread of FOA algorithms to three dimensions, and change its iteration step length, after obtaining improvement
FOA algorithms；
Step (3)：Wavelet Kernel Function is incorporated into SVDD algorithms, established using the characteristic vector of step (1) extraction
WSVDD performance degradation assessment models, and utilize nuclear parameter optimizing of the improved FOA algorithms to WSVDD models；
Step (4)：Characteristic vector is extracted also according to the method for step (1) to bearing Life cycle vibration data, and
As the input of WSVDD models, distance of the characteristic vector apart from hypersphere center is calculated, in this, as the performance degradation assessment of bearing
Index；
Step (5)：Adaptive alarm threshold curve is set, promptly and accurately pre- is made to the early stage degenerate state of bearing
It is alert.
Step (6)：Knot is assessed using based on empirical mode decomposition and the checking of the method for diagnosing faults of Hilbert envelope demodulations
The correctness that fruit is carried out.
Technical scheme more than, can realize following beneficial effect：
(1) present invention is extracted the time domain of bear vibration data and the time-frequency characteristics based on wavelet packet, and is based on monotonicity
Feature selecting is carried out, makes that there is good monotonicity between final evaluation index and fault degree；
(2) Wavelet Kernel Function is incorporated into SVDD algorithms by the present invention, is constructed the performance degradation based on WSVDD algorithms and is commented
Estimate model, compared to LR algorithm, this algorithm only needs the data modeling under a small amount of normal condition, overcomes LR algorithm to failure mould
The dependence of data under formula；Compared to SVDD algorithms, this algorithm is more sensitive to the failure of early stage, more can be timely to early stage event
Barrier makes early warning；
(3) present invention uses improved FOA, using the ratio of supporting vector number and total number of samples as fitness function,
The nuclear parameter of SVDD algorithms is optimized, has both avoided standard FOA optimizing insufficient spaces, the defects of being easily absorbed in local optimum,
The blindness of artificial selection nuclear parameter is eliminated again.
Brief description of the drawings
The experimental provision schematic diagram of Fig. 1 present invention；
The concrete operations flow of Fig. 2 present invention.
Embodiment
For the object, technical solutions and advantages of the present invention etc. are more clearly understood, with reference to embodiments, and with reference to attached
Figure, the present invention is described in more detail.
A kind of rolling bearing performance degradation assessment method based on FOA-WSVDD, operational flowchart is as shown in Fig. 2 described
Method comprises the following steps：
Step (1)：Time domain, the time and frequency domain characteristics vector of vibration data are extracted, and feature selecting is carried out based on monotonicity；
Using the data under the normal condition of bearing 1, its temporal signatures RMS (root mean square), AM (absolute value), SMR (sides are extracted
Root range value), Kurtosis (kurtosis), Skewness (degree of skewness), Peak (peak value), using db8 small echos to data carry out three layers
WAVELET PACKET DECOMPOSITION, the normalized value of eight node energies is obtained, as time-frequency characteristics.Due to bearing in use, performance
Gradually degenerate, and be expendable, so its performance change should be dull over time changes.In order to more accurate high
Effect degraded performance is assessed, using monotonicity as the evaluation index of characteristic vector quality progress feature selecting, feature to
The monotonicity of amount is defined as：
Wherein, x is the characteristic vector after denoising, and K is characterized the length of vector,For unit jump function.
After the monotonicity for calculating each characteristic vector, five higher characteristic vectors of monotonicity are therefrom chosen as final
Characteristic vector.
Step (2)：By the optimizing spatial spread of FOA algorithms to three dimensions, and change its iteration step length, after obtaining improvement
FOA algorithms；
Improved FOA algorithms are for as follows to nuclear parameter optimizing, step：
1) parameter initialization：Initialize population scale sizepop；Maximum iteration maxgen, drosophila colony initial bit
Put X_axis, Y_axis, Z_axis, random flight scope [a, b]；
2) the flight random direction and distance of drosophila individual search food are assigned：
Wherein, β, η are regulatory factor, gen current iteration numbers.In the starting stage of optimizing, in order to increase drosophila population
Diversity, avoid being absorbed in local optimum, the distance of random flight should be increased, now regulatory factor β be more than 1, be designated as β1.Seeking
Excellent second stage, in order to increase low optimization accuracy, the distance of random flight should be reduced, and now regulatory factor β is less than 1, is designated as β2。
3) the distance D of each individual and origin is calculatediAnd flavor concentration judgment value Si：
4) by flavor concentration judgment value SiFlavor concentration discriminant function (fitness function) is substituted into, tries to achieve the taste of drosophila individual
Road concentration, find out the drosophila that flavor concentration is optimal in drosophila population：
Smelli=f (Si)
[bestSmell bestIndex]=min (Smell)
5) best flavors concentration value S and individual respective coordinates X, Y, Z are retained, drosophila colony will fly to the position：
Smellbest=bestSmell
X_axis=X (bestIndex)
Y_axis=Y (bestIndex)
Z_axis=Z (bestIndex)
6) iteration optimizing：Repeat step 2)~4), and judge current best flavors concentration value whether because last time changes
The best flavors concentration value in generation, if performing step 5), when reaching maximum iteration, optimizing terminates.
Step (3)：Wavelet Kernel Function is incorporated into SVDD algorithms, established using the characteristic vector of step (1) extraction
WSVDD performance degradation assessment models, and it is as follows using nuclear parameter optimizing of the improved FOA algorithms to WSVDD models, step：
First, 1) a training sample set X={ x is defined1,...,xn, wherein xi∈Rd(1≤i≤n) is column vector, is led to
Cross nonlinear functionSample characteristics space o ∈ RdIt is mapped to higher-dimension hypersphere space Φ, i.e. φ:X ∈ O → φ (x) ∈ Φ,
Then WSVDD optimization problems are described as：
s.t||φ(xi)-a||2≤r2+ξi,ξi≥0,1≤i≤n
Wherein, a is the center of circle of hypersphere, and r is radius, ξiIt is the relaxation item introduced, C ＞ 0 are control parameters, wrong point of instruction of regulation
Practice sample number (the outer sample number of ball) and r size.
2) Lagrange's equation of optimization problem is：
Wherein α=(α1,...,αn)T>=0, β=(β1,...,βn)T>=0 is that Lagrange multiplier vector above formulas are right respectively
Variable r, a, ξiSeek partial derivative and be set to 0, obtain:
3) dual form of primal problem:
k(xi,xj) it is kernel function, replace inner product to calculate with it, i.e.,Here small echo letter
Number takes Morlet small echos, i.e.,Now kernel function is：
4) using FOA algorithms are improved, to minimize supporting vector number NsvWith total number of samples N ratio FsvAs adaptation
Function is spent, selects optimal nuclear parameter；The dual form of original optimization is convex programming problem, is asked using convex programming problem method for solving
Lagrange multiplier α is taken, the distance for new samples z to the centre of sphere is：
Put f (x)=cv (Confidence Value), the index using CV as bearing performance degradation assessment.
Step (4)：Characteristic vector is extracted also according to the method for step (1) to bearing Life cycle vibration data, and
As the input of WSVDD models, distance of the characteristic vector apart from hypersphere center is calculated, in this, as the performance degradation assessment of bearing
Index, obtain the CV values of bearing Life cycle；
Step (5)：Adaptive alarm threshold curve is set, promptly and accurately pre- is made to the early stage degenerate state of bearing
It is alert.
CV is the parameter of a consecutive variations, represents that equipment deviates the degree of normal condition.Alarm threshold value is set, can be right
The health status of bearing is monitored in real time, and the calculation formula of alarm threshold value is as follows：
In formula：T (t) represents the CV values of t, and mean, std represent to average respectively and standard deviation.Threshold value Th's asks
Solution is divided into 3 stages, and the 1st phase data derives from early stage unfaulty conditions, and threshold value Th is a fixed value, calculation formula such as formula
(1).2nd stage by the T (t) of t compared with the Th (t-1) at t-1 moment, if T (t) is used in the range of Th (t-1)
Formula (2) calculates Th values.If continuous Nu CV values transfinite thereafter, t=t is definedeChanged for performance degradation state
Moment, into phase III, calculation formula such as formula (3).
Step (6)：Knot is assessed using based on empirical mode decomposition and the checking of the method for diagnosing faults of Hilbert envelope demodulations
The correctness that fruit is carried out.
It can be seen from the envelope knowledge of bearing, when some component malfunction of bearing, the envelope spectrum of its impact signal
Can occur the discrete spectral line that amplitude gradually decays at fault characteristic frequency and its frequency multiplication.Empirical mode decomposition is based on so utilizing
With the method for Hilbert envelope demodulations, the envelope spectrum of bearing vibration signal is extracted, the correctness of assessment result is verified.
Claims (3)
1. a kind of rolling bearing performance degradation assessment method based on FOA-WSVDD, specifically includes following steps：
Step (1)：The vibration data under bearing normal condition is obtained, denoising is carried out and normalization pre-processes；Extract vibration data
Time domain, time and frequency domain characteristics vector, and based on monotonicity carry out feature selecting；
Step (2)：By the optimizing spatial spread of FOA algorithms to three dimensions, and change its iteration step length, after being improved
FOA algorithms；
Step (3)：Wavelet Kernel Function is incorporated into SVDD algorithms, the characteristic vector extracted using step (1) establishes WSVDD
Energy degradation assessment model, and utilize nuclear parameter optimizing of the improved FOA algorithms to WSVDD models；
Step (4)：Characteristic vector is extracted according to the method for step (1) to bearing Life cycle vibration data, and is used as WSVDD
The input of model, distance of the characteristic vector apart from hypersphere center is calculated, in this, as the performance degradation assessment index of bearing；
Step (5)：Adaptive alarm threshold curve is set, early warning promptly and accurately is made to the early stage degenerate state of bearing；
Step (6)：Enter using based on empirical mode decomposition and the method for diagnosing faults of Hilbert envelope demodulations checking assessment result
Capable correctness.
2. a kind of rolling bearing performance degradation assessment method based on FOA-WSVDD according to claim 1, it is characterized in that：
The adaptively changing of extension and iteration step length in the step (2) to FOA algorithm optimizing space avoids it from being absorbed in local optimum,
Comprise the following steps：
1) parameter initialization：Initialize population scale sizepop；Maximum iteration maxgen, drosophila colony initial position X_
Axis, Y_axis, Z_axis, random flight scope [a, b]；
2) the flight random direction and distance of drosophila individual search food are assigned：
<mrow>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>X</mi>
<mo>_</mo>
<mi>a</mi>
<mi>x</mi>
<mi>i</mi>
<mi>s</mi>
<mo>+</mo>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>-</mo>
<mi>a</mi>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<mi>r</mi>
<mi>a</mi>
<mi>n</mi>
<mi>d</mi>
<mi>o</mi>
<mi>m</mi>
<mrow>
<mo>(</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
<mo>&rsqb;</mo>
<mo>*</mo>
<msup>
<mi>&beta;</mi>
<mfrac>
<mrow>
<mi>g</mi>
<mi>e</mi>
<mi>n</mi>
</mrow>
<mi>&eta;</mi>
</mfrac>
</msup>
</mrow>
<mrow>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>Y</mi>
<mo>_</mo>
<mi>a</mi>
<mi>x</mi>
<mi>i</mi>
<mi>s</mi>
<mo>+</mo>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>-</mo>
<mi>a</mi>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<mi>r</mi>
<mi>a</mi>
<mi>n</mi>
<mi>d</mi>
<mi>o</mi>
<mi>m</mi>
<mrow>
<mo>(</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
<mo>&rsqb;</mo>
<mo>*</mo>
<msup>
<mi>&beta;</mi>
<mfrac>
<mrow>
<mi>g</mi>
<mi>e</mi>
<mi>n</mi>
</mrow>
<mi>&eta;</mi>
</mfrac>
</msup>
</mrow>
<mrow>
<msub>
<mi>Z</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>Z</mi>
<mo>_</mo>
<mi>a</mi>
<mi>x</mi>
<mi>i</mi>
<mi>s</mi>
<mo>+</mo>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>-</mo>
<mi>a</mi>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<mi>r</mi>
<mi>a</mi>
<mi>n</mi>
<mi>d</mi>
<mi>o</mi>
<mi>m</mi>
<mrow>
<mo>(</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
<mo>&rsqb;</mo>
<mo>*</mo>
<msup>
<mi>&beta;</mi>
<mfrac>
<mrow>
<mi>g</mi>
<mi>e</mi>
<mi>n</mi>
</mrow>
<mi>&eta;</mi>
</mfrac>
</msup>
</mrow>
Wherein, β, η are regulatory factor, gen current iteration numbers；In the starting stage of optimizing, in order to increase the more of drosophila population
Sample, avoid being absorbed in local optimum, the distance of random flight should be increased, now regulatory factor β is more than 1, is designated as β1；In optimizing
Second stage, in order to increase low optimization accuracy, the distance of random flight should be reduced, and now regulatory factor β is less than 1, is designated as β2；
3) the distance D of each individual and origin is calculatediAnd flavor concentration judgment value Si：
<mrow>
<msub>
<mi>D</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<msubsup>
<mi>X</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>Y</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mrow>
<mrow>
<msub>
<mi>S</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>D</mi>
<mi>i</mi>
</msub>
</mfrac>
</mrow>
4) by flavor concentration judgment value SiFlavor concentration discriminant function (fitness function) is substituted into, the taste for trying to achieve drosophila individual is dense
Degree, finds out the drosophila that flavor concentration is optimal in drosophila population：
Smelli=f (Si)
[bestSmellbestIndex]=min (Smell)
5) best flavors concentration value S and individual respective coordinates X, Y, Z are retained, drosophila colony will fly to the position：
Smellbest=bestSmell
X_axis=X (bestIndex)
Y_axis=Y (bestIndex)
Z_axis=Z (bestIndex)
6) iteration optimizing：Repeat step 2)~4), and judge current best flavors concentration value whether due to last iteration
Best flavors concentration value, if performing step 5), when reaching maximum iteration, optimizing terminates.
3. a kind of rolling bearing performance degradation assessment method based on FOA-WSVDD according to claim 1, it is characterized in that：
The foundation of performance degradation assessment model based on WSVDD in the step (3), and using improved FOA algorithms to WSVDD models
Nuclear parameter optimizing, comprise the following steps：
First, 1) a training sample set X={ x is defined1,...,xn, wherein xi∈Rd(1≤i≤n) is column vector, by non-
Linear functionSample characteristics space o ∈ RdIt is mapped to higher-dimension hypersphere space Φ, i.e. φ:X ∈ O → φ (x) ∈ Φ, then
WSVDD optimization problems are described as：
<mrow>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mrow>
<mi>r</mi>
<mo>,</mo>
<mi>c</mi>
<mo>,</mo>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>c</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
</mrow>
s.t ||φ(xi)-a||2≤r2+ξi,ξi≥0,1≤i≤n
Wherein, a is the center of circle of hypersphere, and r is radius, ξiIt is the relaxation item introduced, C ＞ 0 are control parameters, wrong point of training sample of regulation
The size of this number (the outer sample number of ball) and r；
2) Lagrange's equation of optimization problem is：
<mrow>
<mi>L</mi>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>a</mi>
<mo>,</mo>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>&alpha;</mi>
<mo>,</mo>
<mi>&beta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>C</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>|</mo>
<mo>|</mo>
<mi>&phi;</mi>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
<mo>-</mo>
<mi>a</mi>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
</mrow>
Wherein α=(α1,...,αn)T>=0, β=(β1,...,βn)T>=0 is Lagrange multiplier vector, and above formula is respectively to variable
R, a, ξiSeek partial derivative and be set to 0, obtain:
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>a</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleRightArrow;</mo>
<mi>a</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleRightArrow;</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>C</mi>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleRightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
</mrow>
3) dual form of primal problem:
<mrow>
<munder>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
<mi>&alpha;</mi>
</munder>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mi>k</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&alpha;</mi>
<mi>j</mi>
</msub>
<mi>k</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo>&le;</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>&le;</mo>
<mi>C</mi>
<mo>,</mo>
<mn>1</mn>
<mo>&le;</mo>
<mi>i</mi>
<mo>&le;</mo>
<mi>n</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
k(xi,xj) it is kernel function, replace inner product to calculate with it, i.e.,Here wavelet function takes
Morlet small echos, i.e.,Now kernel function is：
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msup>
<mi>x</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>1.75</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
</mrow>
<mi>a</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
4) using FOA algorithms are improved, to minimize supporting vector number NsvWith total number of samples N ratio FsvAs fitness letter
Number, selects optimal nuclear parameter；The dual form of original optimization is convex programming problem, asks for drawing using convex programming problem method for solving
Ge Lang multiplier α, the distance for new samples z to the centre of sphere are：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>1.75</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>a</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&alpha;</mi>
<mi>j</mi>
</msub>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>1.75</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>a</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
Put f (x)=cv (Confidence Value), the index using CV as bearing performance degradation assessment.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710559685.7A CN107562979B (en) | 2017-07-11 | 2017-07-11 | Rolling bearing performance degradation evaluation method based on FOA-WSVDD |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710559685.7A CN107562979B (en) | 2017-07-11 | 2017-07-11 | Rolling bearing performance degradation evaluation method based on FOA-WSVDD |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107562979A true CN107562979A (en) | 2018-01-09 |
| CN107562979B CN107562979B (en) | 2023-07-11 |
Family
ID=60973146
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710559685.7A Active CN107562979B (en) | 2017-07-11 | 2017-07-11 | Rolling bearing performance degradation evaluation method based on FOA-WSVDD |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107562979B (en) |
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108733899A (en) * | 2018-05-02 | 2018-11-02 | 上海理工大学 | The precision machine tool Dynamic performance Optimization method that frequency domain response calculates |
| CN109241915A (en) * | 2018-09-11 | 2019-01-18 | 浙江大学 | The intelligent power plant's pump machine method for diagnosing faults screened based on the steady non-stationary differentiation of vibration signal and feature |
| CZ307847B6 (en) * | 2018-02-14 | 2019-06-19 | ZKL - Výzkum a vývoj a.s. | A method of designing rolling bearings using integrated computer tools |
| CN109974782A (en) * | 2019-04-10 | 2019-07-05 | 郑州轻工业学院 | Equipment fault early-warning method and system based on big data sensitive features optimum option |
| CN110046423A (en) * | 2019-04-12 | 2019-07-23 | 哈工大机器人（合肥）国际创新研究院 | A kind of fault early warning method and system of auxiliary device upstairs |
| CN111597651A (en) * | 2020-04-30 | 2020-08-28 | 上海工程技术大学 | Rolling bearing performance degradation evaluation method based on HWPSO-SVDD model |
| CN111723449A (en) * | 2020-06-30 | 2020-09-29 | 华北科技学院 | Performance degradation evaluation method for constant deceleration braking system of mine hoist |
| CN112765703A (en) * | 2020-12-23 | 2021-05-07 | 桂林电子科技大学 | Dangerous goods wharf structure performance degradation evaluation method |
| CN113139251A (en) * | 2021-04-23 | 2021-07-20 | 桂林电子科技大学 | Variable working condition rolling bearing fault diagnosis method for optimizing theme correlation analysis |
| CN113627088A (en) * | 2021-08-23 | 2021-11-09 | 上海交通大学 | Machine performance degradation evaluation method and system based on gene programming and data fusion |
| CN115901249A (en) * | 2022-11-07 | 2023-04-04 | 昆明理工大学 | Rolling bearing performance degradation evaluation method combining feature optimization and multi-strategy optimization SVDD |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102854015A (en) * | 2012-10-15 | 2013-01-02 | 哈尔滨理工大学 | Diagnosis method for fault position and performance degradation degree of rolling bearing |
| CN105528504A (en) * | 2016-03-01 | 2016-04-27 | 哈尔滨理工大学 | Rolling bearing health condition evaluation method based on CFOA-MKHSVM |
| US20160282229A1 (en) * | 2014-08-28 | 2016-09-29 | Beijing Jiaotong University | Fault Prediction and Condition-based Repair Method of Urban Rail Train Bogie |
| CN106644481A (en) * | 2016-12-27 | 2017-05-10 | 哈尔滨理工大学 | Rolling bearing reliability prediction method based on mathematical morphology and IFOA-SVR |
-
2017
- 2017-07-11 CN CN201710559685.7A patent/CN107562979B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102854015A (en) * | 2012-10-15 | 2013-01-02 | 哈尔滨理工大学 | Diagnosis method for fault position and performance degradation degree of rolling bearing |
| US20160282229A1 (en) * | 2014-08-28 | 2016-09-29 | Beijing Jiaotong University | Fault Prediction and Condition-based Repair Method of Urban Rail Train Bogie |
| CN105528504A (en) * | 2016-03-01 | 2016-04-27 | 哈尔滨理工大学 | Rolling bearing health condition evaluation method based on CFOA-MKHSVM |
| CN106644481A (en) * | 2016-12-27 | 2017-05-10 | 哈尔滨理工大学 | Rolling bearing reliability prediction method based on mathematical morphology and IFOA-SVR |
Non-Patent Citations (2)
| Title |
|---|
| BIN ZHANG ET AL: "Degradation Feature Selection for Remaining Useful Life Prediction of Rolling Element Bearings" * |
| 何青 等: "基于EEMD 和MFFOA-SVM 滚动轴承故障诊断" * |
Cited By (20)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CZ307847B6 (en) * | 2018-02-14 | 2019-06-19 | ZKL - Výzkum a vývoj a.s. | A method of designing rolling bearings using integrated computer tools |
| CN108733899A (en) * | 2018-05-02 | 2018-11-02 | 上海理工大学 | The precision machine tool Dynamic performance Optimization method that frequency domain response calculates |
| CN109241915A (en) * | 2018-09-11 | 2019-01-18 | 浙江大学 | The intelligent power plant's pump machine method for diagnosing faults screened based on the steady non-stationary differentiation of vibration signal and feature |
| CN109241915B (en) * | 2018-09-11 | 2022-03-25 | 浙江大学 | Intelligent power plant pump fault diagnosis method based on vibration signal stability and non-stationarity judgment and feature discrimination |
| CN109974782A (en) * | 2019-04-10 | 2019-07-05 | 郑州轻工业学院 | Equipment fault early-warning method and system based on big data sensitive features optimum option |
| CN109974782B (en) * | 2019-04-10 | 2021-03-02 | 郑州轻工业学院 | Equipment fault early warning method and system based on big data sensitive characteristic optimization selection |
| CN110046423B (en) * | 2019-04-12 | 2023-01-17 | 合肥哈工慈健智能科技有限公司 | Fault early warning method and system for upstairs-going auxiliary device |
| CN110046423A (en) * | 2019-04-12 | 2019-07-23 | 哈工大机器人（合肥）国际创新研究院 | A kind of fault early warning method and system of auxiliary device upstairs |
| CN111597651A (en) * | 2020-04-30 | 2020-08-28 | 上海工程技术大学 | Rolling bearing performance degradation evaluation method based on HWPSO-SVDD model |
| CN111597651B (en) * | 2020-04-30 | 2023-05-02 | 上海工程技术大学 | Rolling bearing performance degradation evaluation method based on HWPSO-SVDD model |
| CN111723449A (en) * | 2020-06-30 | 2020-09-29 | 华北科技学院 | Performance degradation evaluation method for constant deceleration braking system of mine hoist |
| CN111723449B (en) * | 2020-06-30 | 2024-02-20 | 华北科技学院 | Performance degradation evaluation method for constant-deceleration braking system of mine hoist |
| CN112765703A (en) * | 2020-12-23 | 2021-05-07 | 桂林电子科技大学 | Dangerous goods wharf structure performance degradation evaluation method |
| CN112765703B (en) * | 2020-12-23 | 2022-06-21 | 桂林电子科技大学 | Dangerous goods wharf structure performance degradation evaluation method |
| CN113139251B (en) * | 2021-04-23 | 2023-03-14 | 桂林电子科技大学 | Variable working condition rolling bearing fault diagnosis method for optimizing theme correlation analysis |
| CN113139251A (en) * | 2021-04-23 | 2021-07-20 | 桂林电子科技大学 | Variable working condition rolling bearing fault diagnosis method for optimizing theme correlation analysis |
| CN113627088A (en) * | 2021-08-23 | 2021-11-09 | 上海交通大学 | Machine performance degradation evaluation method and system based on gene programming and data fusion |
| CN113627088B (en) * | 2021-08-23 | 2024-04-09 | 上海交通大学 | Machine performance degradation evaluation method and system based on gene programming and data fusion |
| CN115901249A (en) * | 2022-11-07 | 2023-04-04 | 昆明理工大学 | Rolling bearing performance degradation evaluation method combining feature optimization and multi-strategy optimization SVDD |
| CN115901249B (en) * | 2022-11-07 | 2024-02-27 | 昆明理工大学 | Rolling bearing performance degradation evaluation method combining feature optimization and multi-strategy optimization SVDD |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107562979B (en) | 2023-07-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107562979A (en) | A kind of rolling bearing performance degradation assessment method based on FOA WSVDD | |
| CN106682814B (en) | Wind turbine generator fault intelligent diagnosis method based on fault knowledge base | |
| CN107341349B (en) | Method and system for evaluating health of fan, memory and controller | |
| Kusiak et al. | Analyzing bearing faults in wind turbines: A data-mining approach | |
| CN104632521B (en) | A kind of wind power optimization system and method based on drift correction | |
| CN111597651B (en) | Rolling bearing performance degradation evaluation method based on HWPSO-SVDD model | |
| An et al. | Self-learning transferable neural network for intelligent fault diagnosis of rotating machinery with unlabeled and imbalanced data | |
| CN106885697A (en) | The performance degradation assessment method of the rolling bearing based on FCM HMM | |
| Siegel et al. | An auto-associative residual processing and K-means clustering approach for anemometer health assessment | |
| CN109858104A (en) | A kind of rolling bearing health evaluating and method for diagnosing faults and monitoring system | |
| CN108898251A (en) | Consider the marine wind electric field power forecasting method of meteorological similitude and power swing | |
| CN112016251B (en) | Nuclear power device fault diagnosis method and system | |
| CN113570138B (en) | Method and device for predicting residual service life of equipment of time convolution network | |
| Wang et al. | Wind turbines abnormality detection through analysis of wind farm power curves | |
| Loboda et al. | Gas turbine fault diagnosis using probabilistic neural networks | |
| CN102135021B (en) | Method for predicting shaft power of industrial extraction condensing steam turbine | |
| CN112033463A (en) | Nuclear power equipment state evaluation and prediction integrated method and system | |
| Yao et al. | A fault diagnosis method of engine rotor based on random forests | |
| CN109062180A (en) | A kind of oil-immersed electric reactor method for diagnosing faults based on IFOA optimization SVM model | |
| Baraldi et al. | An ensemble approach to sensor fault detection and signal reconstruction for nuclear system control | |
| CN104218571B (en) | A kind of running status appraisal procedure of wind power plant | |
| CN111191832A (en) | Typhoon disaster power distribution network tower fault prediction method and system | |
| Yang et al. | Twin Broad Learning System for Fault Diagnosis of Rotating Machinery | |
| CN104268662B (en) | A kind of settlement prediction method based on step-by-step optimization quantile estimate | |
| Yürüşen et al. | Probability density function selection based on the characteristics of wind speed data |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |