CN109632312A - Bearing combined failure diagnostic method based on multiple constraint Algorithms of Non-Negative Matrix Factorization - Google Patents
Bearing combined failure diagnostic method based on multiple constraint Algorithms of Non-Negative Matrix Factorization Download PDFInfo
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Abstract
A kind of bearing combined failure diagnostic method based on multiple constraint Algorithms of Non-Negative Matrix Factorization.Fault signature separation is carried out present invention is generally directed to the combined failure of rotating machinery middle (center) bearing and is extracted, increase plate storehouse-vegetarian rattan (Itakura-Saito on the basis of traditional Algorithms of Non-Negative Matrix Factorization, IS) divergence constraint is constrained with determinant, is enhanced local feature information and is guaranteed the uniqueness of decomposition result；Signal after time-frequency conversion is subjected to multiple constraint Non-negative Matrix Factorization, and reconstructs characteristic component in lower-dimensional subspace；Reconfiguration waveform index is constructed, filters out the characteristic component for meeting threshold requirement as separation signal；Demodulation process is carried out to separation signal, fault characteristic frequency is obtained, determines abort situation, realizes the combined failure diagnosis of bearing.
Description
Technical field
The present invention relates to a kind of Method for Bearing Fault Diagnosis, in particular to a kind of to be based on multiple constraint Algorithms of Non-Negative Matrix Factorization
Bearing combined failure diagnostic method, belong to fault diagnosis technology field.
Background technique
In industrialized modern society, rolling bearing is as one kind general zero there will necessarily be in rotation class mechanical equipment
Part, safe operation carry out status monitoring to bearing and failure are examined for ensureing that economic society stable development is of great significance
Disconnected is the important channel for ensureing its safe operation.
Analysis method based on vibration signal has been widely used in the fault diagnosis of mechanical equipment, because of vibration letter
Number equipment running status information abundant is generally comprised, and very easy acquisition is acquired by acceleration transducer.Axis
It holds when being run under actual working conditions, often multiple failures occur simultaneously, and multiple fault characteristic signals intercouple,
It is more complicated than single point failure to diagnose difficulty.At present for combined failure diagnostic method it is relatively fewer, model relative to not at
It is ripe.Therefore, the multiple faults source vibration signal monitored is handled, therefrom isolates combined failure feature, carries out shape in time
State identification and fault pre-alarming are of great significance to mechanical equipment normal operation and system health management.
For multiple source-coupled signal, there are some traditional separation methods, such as: empirical mode decomposition, local mean value point
The methods of solution, variation mode decomposition.Algorithms of Non-Negative Matrix Factorization is realized simple and is divided as a kind of new feature extracting method
Solution form and decomposition result have more physical significance, the defect of some algorithms of tradition are overcome, in intelligence learning, image procossing, machine
The fields such as device vision and information retrieval are widely used.In blind source separating problem, compared to independent component analysis and sparse component
Analysis, the constraint that Non-negative Matrix Factorization needs is less, and convergence is very fast, and decomposition efficiency is higher.However, in rotating machinery field, by
In working condition complexity, the vibration signal signal-to-noise ratio of generation is low, and characteristic information is fainter, and information is mutually dry between each source signal
It disturbs, traditional Algorithms of Non-Negative Matrix Factorization bound term is insufficient, causes data redundancy larger, fault characteristic information is not easy to be extracted.
Summary of the invention
The object of the present invention is to provide a kind of bearing combined failures based on multiple constraint Algorithms of Non-Negative Matrix Factorization to examine
Disconnected method, to solve above-mentioned technical problem of traditional Algorithms of Non-Negative Matrix Factorization in the diagnosis of bearing combined failure.
To achieve the above object, the technical solution adopted by the present invention is a kind of based on multiple constraint Algorithms of Non-Negative Matrix Factorization
Bearing combined failure diagnostic method, this method acquire bearing vibration signal including the use of sensor, to bearing vibration
Signal carries out liter dimension processing and to the eigenmatrix after liter dimension using the processing of multiple constraint Algorithms of Non-Negative Matrix Factorization, characteristic component
Reconstruct, to after reconstruct signal carry out demodulation process, extract the fault signature of bearing.
S1 acquires bearing vibration signal；
The acquisition of the vibration signal is acquired by the acceleration transducer being placed on bearing block vertical direction；
S2 carries out liter dimension to bearing vibration signal and handles；
Here liter dimension is carried out to vibration signal using formula (1) to handle:
S (t, f)=∫ x (t+ τ) w (τ) exp (- 2j π f τ) d τ (1)
Wherein, t is the time, and f is frequency, and x (t) is time-domain signal to be processed, and w (t) is window function；
S3 handles the eigenmatrix after liter dimension using multiple constraint Algorithms of Non-Negative Matrix Factorization；
Traditional Non-negative Matrix Factorization model are as follows: the nonnegative matrix generated at randomIt resolves intoWithIt is set to meet following formula:
Vm×n=Wm×rHr×n (2)
Wherein: m is the dimension of matrix, and n is sample number, and r is the order of matrix dimensionality reduction, and matrix W and H are respectively basic matrix and are
Matrix number, and guarantee nonnegativity；
Multiple constraint Algorithms of Non-Negative Matrix Factorization the following steps are included:
The construction of 3.1 high dimensional feature matrixes；Liter dimension is carried out to vibration signal using formula (1) to handle, and obtains local feature
Enhanced high dimensional feature matrix
The processing of 3.2 multiple constraint Algorithms of Non-Negative Matrix Factorization；Select localization more preferably plate storehouse-vegetarian rattan (Itakura-
Saito, IS) determinant of uniqueness constrains the objective function new as Non-negative Matrix Factorization after divergence constraint and determining is decomposed；
IS divergence restricted model are as follows:
Definition ties up column vector W by n m1,W2,...WnThe space opened is denoted as P (W), then the volume of P (W) can be by following formula table
Show:
When vol (W) minimum, obtained correspondence vector W1,W2,...WnIt can uniquely determine, this is determinant constraint mould
Type；
New objective function are as follows:
Wherein: α, β are balance parameters；
Since the constraint of IS divergence and determinant constraint are in objective function optimization equation, it is by the update of constantly iteration
The optimization of bound term can be achieved, and not only local feature is enhanced decomposition result, while decomposition result has uniqueness.
The reconstruct of S4 characteristic component；
4.1 reconstruct multiple constraint Non-negative Matrix Factorization treated basic matrix W and coefficient matrix H, obtain characteristic component
Reconfiguration waveform；
4.2 define reconfiguration waveform index R；
In statistics, related coefficient can characterize similar degree between signal；Kurtosis (Kurtosis) can be effective
Ground detects transient fault impact ingredient and its band position in signal, and can identify the resonance frequency comprising transient fault impact
Band；Building reconfiguration waveform index R is the two product form, model are as follows:
R=| C | K (6)
Wherein: C is the related coefficient of signal x and y, and E [] represents mathematic expectaion；When C is positive number, indicate to be positively correlated；
Otherwise, it means that negatively correlated；According to Schwartz inequality, it is known that | C |≤1；The kurtosis of K expression signal；It can according to formula (6)
Know, reconfiguration waveform index R is bigger, and the characteristic information that signal is included is abundanter, therefore can be using given threshold as screening reconstruct point
Standard from signal；
4.3, which filter out waveform index, meets threshold requirement as separation signal；
S5 carries out demodulation process to separation signal；
Signal after characteristic component is reconstructed carries out demodulation process, obtains failure-frequency, with theory characteristic frequency comparison from
And determine abort situation.
Compared with prior art, the invention has the following beneficial effects:
1, the present invention is in traditional Algorithms of Non-Negative Matrix Factorization, the characteristics of for bearing combined failure signal, lead-in plate storehouse-
The constraint of vegetarian rattan (Itakura-Saito, IS) divergence and determinant constrain the objective function new as algorithm；Further enhance part
Change characteristic information, reduce the existence of redundant due to interfering with each other between multi-source component, keeps decomposition dimensionality reduction effect more preferable, guarantee simultaneously
The uniqueness of decomposition result, can obtain more preferably quality reconstruction.
2, comprehensively consider signal similarity degree, impact degree, mark of the building reconfiguration waveform index R as screening separation signal
Standard can efficiently extract characteristic information separation signal abundant, filter redundancy, be subsequent fault signature extraction step
Effective guarantee is provided.
Detailed description of the invention
Fig. 1 is the bulk flow of the bearing combined failure diagnostic method of the invention based on multiple constraint Algorithms of Non-Negative Matrix Factorization
Cheng Tu.
Fig. 2 is that there are the time domain waveform of vibration signal when combined failure and envelope frequency spectrum figures for practical bearing of the present invention.
Fig. 3 is the spectrogram that the method for the present invention carries out that demodulation process is obtained to isolated reconstruction signal.
Fig. 4 is to compare experiment using traditional non-negative matrix factorization method to verify the method for the present invention validity, right
Isolated reconstruction signal carries out the spectrogram that demodulation process obtains.
Specific embodiment
The invention will be further described with application example with reference to the accompanying drawing.
Fig. 1 is the bulk flow of the bearing combined failure diagnostic method of the invention based on multiple constraint Algorithms of Non-Negative Matrix Factorization
Cheng Tu.It is described in detail below with reference to flow chart and application example.
(1) by the acceleration transducer that is placed in bearing block vertical direction, horizontal direction or axial direction to vibration signal
It is acquired, obtains vibration acceleration signal as signal S to be analyzed；
(2) according to time-frequency conversion model:
S (t, f)=∫ x (t+ τ) w (τ) exp (- 2j π f τ) d τ (9)
The signal S being analysed to carries out a liter dimension and handles to obtain eigenmatrix V, and V is as multiple constraint Non-negative Matrix Factorization at this time
Input matrix；
(3) Jiang Bancang-vegetarian rattan (Itakura-Saito, IS) divergence constraint and determinant constraint are used as Non-negative Matrix Factorization
New objective function:
Gradient descent method is selected, constantly iteration updates to new objective function, until meeting stopping criterion for iteration
Realize the optimization of bound term；
(4) after handling according to multiple constraint Algorithms of Non-Negative Matrix Factorization, basic matrix W and coefficient matrix H are obtained, by the two low
Dimension space reconstruct, obtains the reconfiguration waveform of characteristic component；
(5) it calculates each reconfiguration waveform index R and waveform index R is filtered out according to original signal waveform parameter threshold value
Meet the reconstruction signal of threshold requirement as separation signal；
(6) separation signal is subjected to demodulation process, obtains failure-frequency, that is, can determine abort situation, realizes combined failure
Diagnosis.
Fig. 2 is that there are the time domain waveform of vibration signal when combined failure and envelope frequency spectrum figures for practical bearing of the present invention；Choosing
Selecting bearing designation is NTN N204 type cylinder roller bearing, there are width is 0.5mm on outer ring and rolling element, depth is
The accident defect of 0.15mm；Wherein sample frequency is 100kHz, interception 0.5s time slice analysis；Motor speed is set as
900r/min, according to bearing structure parameter and outer ring, rolling element defect characteristic frequency calculation formula:
Outer ring defect characteristic frequency (fo):
Rolling element defect characteristic frequency (fb):
Wherein: z is rolling element number, and d is rolling element diameter, and D is the outer pitch diameter of bearing, and α is rolling element and retainer
Between contact angle, frTurn frequency for motor.
It is respectively 60Hz, 74Hz that housing washer and rolling element theory characteristic frequency, which is calculated,；
From time domain waveform it can be seen that shock pulse ingredient, but cyclophysis is not obvious under influence of noise, can not
Obtain the useful status information of bearing.In envelope frequency spectrum figure, only outer ring defect characteristic can be identified, it is special to roll volume defect
Sign is flooded by noise contribution, it is difficult to be identified.It handles using based on multiple constraint Algorithms of Non-Negative Matrix Factorization, is reconstructed according to above-mentioned steps
Signal is separated, the envelope frequency spectrum figure of separation signal is obtained.
Fig. 3 is to carry out the envelope frequency spectrum figure that demodulation process obtains to the separation signal of reconstruct in the present invention；As can be seen that
To two source signals ingredients, respectively 60Hz and 74Hz and its higher hamonic wave, two kinds of frequency contents just correspond to outer ring and rolling
Kinetoplast defect characteristic frequency, that is, separated mixed signal, realized fault diagnosis.
Fig. 4 is to compare the envelope frequency spectrum figure that experiment obtains using traditional Algorithms of Non-Negative Matrix Factorization, can from Fig. 4
Out, after traditional NMF algorithm process, the realization of bearing combined failure signal is not efficiently separated, only outer ring fault signature quilt
It extracts, rolling element fault signature ingredient is submerged.Therefore, the method for the present invention is again demonstrated to examine for bearing combined failure
Disconnected validity.
Claims (3)
1. a kind of bearing combined failure diagnostic method based on multiple constraint Algorithms of Non-Negative Matrix Factorization, it is characterised in that: this method
Bearing vibration signal is acquired including the use of sensor；A liter dimension processing is carried out to bearing vibration signal；After liter dimension
Eigenmatrix is handled using multiple constraint Algorithms of Non-Negative Matrix Factorization；The reconstruct of characteristic component；Signal after reconstruct is demodulated
Processing, extracts the fault signature of bearing；
S1 acquires bearing vibration signal；
The acquisition of the vibration signal passes through the acceleration transducer that is placed in bearing block vertical direction, horizontal direction or axial direction
It is acquired；
S2 carries out liter dimension to bearing vibration signal and handles；
Here liter dimension is carried out to vibration signal using formula (1) to handle:
S (t, f)=∫ x (t+ τ) w (τ) exp (- 2j π f τ) d τ (1)
Wherein, t is the time, and f is frequency, and x (t) is time-domain signal to be processed, and w (t) is window function；
S3 handles the eigenmatrix after liter dimension using multiple constraint Algorithms of Non-Negative Matrix Factorization；
The reconstruct of S4 characteristic component；
4.1 reconstruct multiple constraint Non-negative Matrix Factorization treated basic matrix W and coefficient matrix H, obtain the reconstruct of characteristic component
Waveform；
4.2 define reconfiguration waveform index R, and calculate the R value of each group of reconstruction signal；
4.3, according to original signal waveform parameter threshold value, filter out the reconstruction signal conduct that waveform index R meets threshold requirement
Separate signal；
S5 carries out demodulation process to separation signal；
Signal after characteristic component is reconstructed carries out demodulation process, obtains failure-frequency, with theory characteristic frequency comparison to really
Determine abort situation.
2. a kind of bearing combined failure diagnosis side based on multiple constraint Algorithms of Non-Negative Matrix Factorization according to claim 1
Method, it is characterised in that: lead-in plate storehouse-vegetarian rattan (Itakura-Saito, IS) divergence on the basis of traditional Algorithms of Non-Negative Matrix Factorization
Constraint and determinant constrain the objective function new as algorithm.
Traditional Non-negative Matrix Factorization model are as follows: the nonnegative matrix generated at randomIt resolves intoWithIt is set to meet following formula:
Vm×n=Wm×rHr×n (2)
Wherein: m is the dimension of matrix, and n is sample number, and r is the order of matrix dimensionality reduction, and matrix W and H are respectively basic matrix and coefficient square
Battle array, and guarantee nonnegativity；
Plate storehouse-vegetarian rattan (Itakura-Saito, IS) divergence constraint, can enhance local feature information, reduce phase between multi-source component
The existence of redundant mutually interfered keeps decomposition dimensionality reduction effect more preferable；IS dispersion models are as follows:
Determinant constraint is selected, guarantees that decomposition result has uniqueness, obtains more preferably quality reconstruction；Definition is by n m dimension column arrow
Measure W1,W2,...WnThe space opened is denoted as P (W), then the volume of P (W) can be expressed from the next:
When vol (W) minimum, obtained correspondence vector W1,W2,...WnIt can uniquely determine；
After increasing the constraint of IS divergence and determinant constraint, new objective function expression formula are as follows:
Wherein: α, β are balance parameters；
It, can be real by the update of constantly iteration since the constraint of IS divergence and determinant constraint are in objective function optimization equation
The optimization of existing bound term, and not only local feature is enhanced decomposition result, while decomposition result has uniqueness.
3. a kind of bearing combined failure diagnosis side based on multiple constraint Algorithms of Non-Negative Matrix Factorization according to claim 1
Method, it is characterised in that: define reconfiguration waveform index R, the separation signal of the reconstruct comprising feature-rich information is filtered out according to threshold value.
In statistics, related coefficient can characterize similar degree between signal；Kurtosis (Kurtosis) can be examined effectively
Transient fault impact ingredient and its band position in signal are surveyed, and can identify the resonance bands comprising transient fault impact；
Building reconfiguration waveform index R is the two product form, model are as follows:
R=| C | K (6)
Wherein: C is the related coefficient of signal x and y, and E [] represents mathematic expectaion；When C is positive number, indicate to be positively correlated；Conversely,
Then indicate negatively correlated；According to Schwartz inequality, it is known that | C |≤1；The kurtosis of K expression signal；According to formula (6) it is found that reconstruct
Waveform index R is bigger, and the characteristic information that signal is included is abundanter, therefore separation signal can be reconstructed using given threshold as screening
Standard；According to original signal waveform parameter threshold value, the reconstruction signal conduct point that waveform index R meets threshold requirement is filtered out
From signal；Separation signal after reconstruct is subjected to demodulation process you can get it fault signature, determines abort situation.
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| CN110319995A (en) * | 2019-08-14 | 2019-10-11 | 清华大学 | Firer's shock response data time-frequency spectrum analysis method |
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| CN112857804A (en) * | 2021-02-09 | 2021-05-28 | 广东海洋大学 | Rolling bearing fault diagnosis method, device, medium and computer equipment |
| CN114942133A (en) * | 2022-05-20 | 2022-08-26 | 大连理工大学 | Optimal rank non-negative matrix factorization-based early fault diagnosis method for planetary gearbox |
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| CN110426569A (en) * | 2019-07-12 | 2019-11-08 | 国网上海市电力公司 | A kind of transformer acoustical signal noise reduction process method |
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| CN110319995A (en) * | 2019-08-14 | 2019-10-11 | 清华大学 | Firer's shock response data time-frequency spectrum analysis method |
| CN112464712A (en) * | 2020-10-20 | 2021-03-09 | 浙江大学 | Rotating machine fault diagnosis method based on blind extraction algorithm |
| CN112464712B (en) * | 2020-10-20 | 2022-07-22 | 浙江大学 | Rotating machine fault diagnosis method based on blind extraction algorithm |
| CN112857804A (en) * | 2021-02-09 | 2021-05-28 | 广东海洋大学 | Rolling bearing fault diagnosis method, device, medium and computer equipment |
| CN112857804B (en) * | 2021-02-09 | 2022-06-17 | 广东海洋大学 | Rolling bearing fault diagnosis method, device, medium and computer equipment |
| CN114942133A (en) * | 2022-05-20 | 2022-08-26 | 大连理工大学 | Optimal rank non-negative matrix factorization-based early fault diagnosis method for planetary gearbox |
| CN114942133B (en) * | 2022-05-20 | 2023-04-14 | 大连理工大学 | Optimal rank non-negative matrix factorization-based early fault diagnosis method for planetary gearbox |
| CN115356108A (en) * | 2022-10-10 | 2022-11-18 | 成都阿普奇科技股份有限公司 | Method and device for diagnosing mechanical fault of modulation high-order horizontal extrusion transformation |
| CN115356108B (en) * | 2022-10-10 | 2023-02-10 | 成都阿普奇科技股份有限公司 | Method and device for diagnosing mechanical fault of modulation high-order horizontal extrusion transformation |
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