CN109253882A - A kind of rotor crack fault diagnostic method based on variation mode decomposition and gray level co-occurrence matrixes - Google Patents
A kind of rotor crack fault diagnostic method based on variation mode decomposition and gray level co-occurrence matrixes Download PDFInfo
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Abstract
The present invention provides a kind of rotor crack fault diagnostic method based on variation mode decomposition and gray level co-occurrence matrixes, belongs to crack fault diagnostic field.It comprises the step of: acquisition vibration signal；Collected signal is subjected to variation mode decomposition；Symmetrical polar image is generated to each IMF component；Gray level image is converted by symmetrical polar image；Grayscale image generates gray level co-occurrence matrixes, extracts image texture characteristic as characteristic parameter；Choose the characteristic statistic entropy of gray level co-occurrence matrixes；Seek i-th of IMF component of a certain operating condition；The mean entropy in 4 directions of the sample under corresponding states is sought respectively；Acquisition is several to diagnostic sample, extracts feature vector；Calculate mahalanobis distance；Compare the d of sample to be tested1,d2Size, comprehensive distance smaller's is exactly to the corresponding state of diagnostic sample.The present invention overcomes simple using gray level co-occurrence matrixes in the deficiency of rotor crack fault signal processing, can complete rotor crack fault diagnosis very well.
Description
[technical field]
It is specifically a kind of to be based on variation mode decomposition and gray scale symbiosis square the present invention relates to rotary machinery fault diagnosis field
The method of the rotor crack fault diagnosis of battle array.
[background technique]
With industrialization paces accelerate, rotating machinery using more and more extensive.Such mechanical equipment, as space flight is started
Machine, wind-driven generator, rocket engine engine etc., play important in the industrial circles such as aviation, the energy, traffic, petrochemical industry
Role.
It, can be before rotor be installed life's work, by super for rotor machining process or material self-defect
Technology of acoustic wave reliably detects out that whether there are cracks.The core component rotor of rotating machinery is often because in the operating conditions such as load is changeable
Under, it is influenced by vertiginous thermal stress and mechanical stress and generates stress and concentrate, development quickly is tired axis crackle.
If handled without discovery in time, crackle will be because of being extended intensification, mutation by stress alternation so that cause fearful disconnected
Split the accident with fatal crass.
Since structure is complicated and equipment lotus root connection property is strong for above-mentioned rotating machinery, early failure of rotor vibration signal shows as non-
Linearly, it non-stationary property and is easily submerged in strong noise environment, significantly impacts the extraction of rotor fault feature.In recent years,
Many scholars at home and abroad are directed to the detection and diagnosis of rotor fault signal, have done a large amount of research work.
The method of currently used mode decomposition has: wavelet decomposition, empirical mode decomposition, and local mean value is decomposed.Although this
A little mode decomposition methods achieve certain progress in fault diagnosis field, but its there is also shortcomings.Wavelet decomposition
It comforms and selects suitable wavelet basis function and Decomposition order in multi-wavelet bases.Empirical mode decomposition does not have mathematical theory basis,
Algorithm is gradually decomposed using recurrence screening, can not backward error correction, and there are modal overlap phenomenons.Local mean value Decomposition iteration
It is computationally intensive, it is also easy to generate end effect.
Variation mode decomposition (Variational Mode Decomposition, VMD), is a kind of predetermined scale
Nonstationary random response method, this method can be divided into unstable sophisticated signal K preset amplitude-modulation frequency-modulation signal.Variation mould
State, which is decomposed, uses frequency domain non-recursive fashion Solve problems, and Decomposition Accuracy is high and can preferably avoid modal overlap phenomenon.Gray scale
The textural characteristics of co-occurrence matrix energy accurate description image, the texture image identification technology based on gray level co-occurrence matrixes is in medicine figure
Picture, weather nephogram are widely applied in the identification of the grain of wood.
[summary of the invention]
Unstable, non-linear for cracked rotor vibration displacement signal, fault signature difficulty is extracted, and is lacked at failure initial stage
Collection and arrangement to sample, the present invention provide a kind of rotor crack fault based on variation mode decomposition and gray level co-occurrence matrixes
Diagnostic method.
In order to achieve the above object, the present invention is adopted the following technical scheme that
The critical speed of rotor-support-foundation system is measured first, then makes rotor-support-foundation system in 1.5 times of critical speeds of actual speed
Under operating condition, following processing are carried out:
Step 1: the radial direction on current vortex sensor and infrared electro speed probe acquisition rotor at any is respectively adopted
Vibration signal and rotor speed signal, acquisition have N number of sample under cracked rotor and flawless rotor two states；
Step 2: collected signal { x (n) } being subjected to variation mode decomposition, i.e., K are sought to the vibration signal of rotor
Mode function uk(t), K IMF component is obtained；
Step 3: symmetrical polar image is generated to each IMF component；
Step 4: converting gray level image for symmetrical polar image；
Step 5: grayscale image generates gray level co-occurrence matrixes, extracts image texture characteristic as characteristic parameter；
Step 6: choosing the characteristic statistic entropy of gray level co-occurrence matrixes, take e1,e2,a3,a4Respectively represent 0 °, 45 °, 90 °,
The entropy in 135 ° of directions；
Step 7: setting two operating conditions of rotor-support-foundation system as j, wherein j=1 represents flawless axis, and j=2 represents crackle axis, right
In the feature vector of i-th of IMF component of a certain operating condition be just Hji=[ei1,ei2,ei3,ei4], it is 4 dimensional vectors；
Step 8: and then 0 ° of N number of sample under corresponding states is asked respectively, 45 °, 90 °, the average value of the entropy in 135 ° of directions,
Corresponding states feature reference vectors are obtained, are as follows:
Step 9: acquisition to diagnostic sample several, also pass through the above process, extract feature vector Hji=[ei1,
ei2,ei3,ei4]
Step 10: passing through formulaCalculate separately the feature of i-th of IMF of diagnostic data
Mahalanobis distance between vector and the state reference feature vector of i-th of IMF of j state；
Step 11: calculating state comprehensive distance, the comprehensive distance of sample to be tested characteristic sequence and each state reference signal,
And give corresponding weighting coefficient b1, bk, calculating formula are as follows: dj=b1·dj1+b2·dj2+…+bk·djk；
Step 12: comparing the d of sample to be tested1,d2Size, determine comprehensive distance smaller is exactly to diagnostic sample pair
The state answered.
In the present invention, further, in the step (2), the step of variation mode decomposition, includes:
Step 2.1: initializationN, in formula, ukTo decompose K obtained modal components, ωkFor each mould
The corresponding center frequency of state component, ^ are the frequency domain representation using Parseval/Plancherel Fourier's equilong transformation, and λ is
Lagrange multiplier, n are the number of iterations；
Step 2.2: updatingWith
Step 2.3: update operator
Step 2.4: step 2.2~2.4 are repeated, until meet the condition of convergence,It gives
Determine discrimination precision ∈ > 0, end loop exports K IMF component.
In the present invention, further, symmetrical polar image is converted in the step 4 specific method of gray level image
Are as follows: symmetrical polar image array W is set, size is m × n, and the element value of a row b column is A(a,b), symmetrical polar figure
Maximum value A as inmaxIt is corresponding with tonal gradation 255, minimum value AminIt is corresponding with tonal gradation 0, gray scale is converted by following formula
Value is
Unit8 is 8 rounding operation symbols of no symbol, and operation result is the integer between 0~255.
In the present invention, further, in the step 5 method particularly includes: the picture for being B from the grey level on grayscale image
First position (x, y) is set out, and statistics is s at a distance from it, and the pixel position (x+Dx, y+Dy) that grey level is C occurs simultaneously
Frequency P (B, C, s, θ).
P (B, C, s, θ)=[(x, y), (x+Dx, y+Dy) | f (x, y)=B, f (x+Dx, y+Dy)=C] } (19)
In formula (19), B, C=0,1,2 ..., 255 be grey level, Dx, Dy be respectively both horizontally and vertically on position
Setting offset, s is the step-length of grayscale image matrix, and θ is the direction that grayscale image matrix generates, take 0 °, 45 °, 90 °, 135 ° of 4 sides
To,
Pass through normalization process process by formula (20)
Wherein, g (B, C) indicates that P (B, C) matrix passes through the matrix that Regularization process obtains.
In the present invention, further, entropy is calculated as follows in the step 6:
Take s=1, e1,e2,a3,a4Respectively represent 0 °, 45 °, 90 °, the entropy in 135 ° of directions.
Due to using above-mentioned technological means, compared with the prior art, the present invention has the following beneficial effects:
1. the method for the present invention combines the advantage of variation mode decomposition and gray level co-occurrence matrixes respectively, used variation mould
State decomposition method decomposes vibration signal, effectively reduces reactive component and modal overlap, and arrangement entropy is combined to calculate letter
Singly, the features such as noise resisting ability is strong, from each modal components middle (center) bearing fault signature of multiple dimensioned angle extraction, overcomes simple use
Gray level co-occurrence matrixes can also complete rotor crack in noise jamming in the deficiency of rotor crack fault signal processing very well
Fault diagnosis.
2. the present invention using variation mode decomposition to crackle rotor fault signal carry out mode decomposition, avoid well through
Test the modal overlap phenomenon occurred when mode decomposition and local mean value decomposition, end effect phenomenon.
[Detailed description of the invention]
Fig. 1 rotor crack fault diagnostic method flow chart of the present invention.
Fig. 2 is variation mode decomposition algorithm flow chart.
Fig. 3 is the schematic diagram of symmetrical polar method.
Fig. 4 is symmetrical polar figure and grayscale image corresponding relationship.
Fig. 5 is 4 generation directions of gray level co-occurrence matrixes.
Fig. 6 is flawless rotor time-domain signal.
Fig. 7 is cracked rotor time-domain signal.
[specific embodiment]
The present invention is further illustrated below by way of specific embodiment and in conjunction with attached drawing.
Based on the method for the rotor crack fault of variation mode decomposition and gray level co-occurrence matrixes diagnosis, flow chart is shown in Fig. 1
It is shown, specific steps are as follows:
Step 1: the radial direction on current vortex sensor and infrared electro speed probe acquisition rotor at any is respectively adopted
Vibration signal and rotor speed signal, sample frequency 2KHz acquire 512 points, and acquisition has cracked rotor and flawless rotor two
N number of sample under kind state；
Step 2: collected signal { x (n) } being subjected to variation mode decomposition, collected signal { x (n) } is passed through into change
Divide mode decomposition to obtain K IMF component, is set as ui, i=1,2, K.Each IMF includes that corresponding mode is special
Reference breath, then extracting feature from K IMF, so that it may show original signal xt(n) feature.
Variation mode decomposition algorithm flow chart is shown in Fig. 2, in order to which mode decomposition method of the invention is better described, illustrates below
The basic principle of variation mode decomposition:
Define an amplitude-modulation frequency-modulation signal is defined as:
uk(t)=Ak(t)cos[φk(t)] (1)
In formula (1), φkIt (t) is a non-decreasing phase function, φk(t) derivative is more than or equal to zero；Signal envelope value
Ak(t) it is more than or equal to zero, φk(t) speed of the speed changed much larger than the change of instantaneous frequency and envelope value.In other words, exist
In one sufficiently long region in [t- δ, t+ δ], 2 π of δ ≈/φ 'k(t), uk(t) it can be used as and possess certain temporal frequency domain and amplitude
Pure harmonic signal.
Its detailed process is divided into two big steps
(1) under defined frame constraint, Variation Model is constructed.
1. by each mode function uk(t) Hilbert-Huang Transform is carried out, its respective unilateral frequency spectrum analytic signal is obtained:
2. for each mode uk(t), if its centre frequency isThe two is multiplied, is adjusted in estimating accordingly
Frequency of heart, to filter out " base band ":
3. finally calculating square of demodulated signal time gradient L2- norm, and utilize the analysis of Gaussian smoothing demodulated signal
Method obtains the finite bandwidth of each mode function.
Then, constraint variation condition are as follows:
In formula (4): f (t) is original input signal, { uk}={ u1…uk, { ωk}={ ω1…ωkRespectively indicate by
The K IMF (Intrinsic Mode Function) of VMD and corresponding centre frequency.
(2) the solution of constraint variation model problem.
For convenience of solution, the constrained function of target is changed into free objective function optimization problem, passes through introducing
Secondary penalty factor α and Lagrange operational form λ (t).Wherein secondary penalty factor α improves convergence under Gauusian noise jammer and protects
Signal reconstruction precision is demonstrate,proved, Lagrange operational form λ (t) allows constraint condition with more stringency.
Then augmented Lagrange multiplier formula function are as follows:
It is alternately updated by two direction of multiplication operatorλn+1Seek formula augmented Lagrange multiplier formula function
As a result, being the saddle point of formula (5).This method is multiplication operator alternating direction method (alternate direction method of
Multipliers, ADMM).
Then update modeIt is exactly a minimum Solve problems, expression formula are as follows:
Under L2- norm, above formula is converted to by frequency domain using Parseval/Plancherel Fourier equilong transformation:
In formula (7) first item, according to Hermitain symmetry characteristic, with ω-ωkω is substituted, formula is transformed into non-negative
The form of frequency separation integral:
Obtain the update of k-th mode, that is, the solution of optimization problem are as follows:
It is also minimum optimization problem, description that similarly center frequency domain, which updates, are as follows:
Formula (10) is for conversion into the form of non-negative frequency separation integral:
Then centre frequency is in frequency domain more new-standard cement are as follows:
Operator λn+1More new-standard cement are as follows:
In formula (13)For the Lagrange multiplier operator before update；τ is step-length.
Then iteration updates uk, ωk, formula until meeting the following condition of convergence:
∈ is given judgement precision (∈ > 0), is also preset convergence error.
IMF in frequency domain is done inverse fourier transform processing, removes the data of end effect, obtains IMF points in time domain
Amount.
Step 3: symmetrical polar image being generated to each IMF component, Fig. 3 is the schematic diagram of symmetrical polar method.
For each IMF component uiIn, the amplitude of t moment is Ai, the amplitude at t+L moment is At+L, substitute into formula and be converted into
Polar coordinate spacePoint
R (t) is polar radius in formula (15)~(17), and θ (t) is polar coordinates counterclockwise along the angle of initial line rotation
Degree,It is polar coordinates clockwise along the angle of initial line rotation, AmaxFor component uiMaximum value, AminFor component uiMinimum
Value, L are time interval, and n is plane of mirror symmetry number, and θ is initial rotation angle, and g is angle magnification factor.
Step 4, gray level image is converted by symmetrical polar image, extracts image texture characteristic as characteristic parameter.
Gray level image is a two-dimensional data matrix, and the subscript of matrix element is answered with its ranks coordinate pair in the picture,
The value of element represents the brightness value of corresponding position, and taking tonal gradation is 256 grades, the maximum value A in symmetrical polar imagemaxWith
Tonal gradation 255 is corresponding, minimum value AminIt is corresponding with tonal gradation 0.
If claiming polar coordinate image matrix W, size is m × n, and the element value of a row b column is A(a,b),
Being converted into gray value by formula (18) is
Unit8 is 8 rounding operation symbols of no symbol, and operation result is the integer between 0~255.
It is polar diagram and grayscale image corresponding relationship such as Fig. 4.
Step 5, gray level co-occurrence matrixes are generated according to grayscale image, extracts characteristic parameter.
From the pixel position that the grey level on grayscale image is B, (x, y), statistics are s, grey level at a distance from it
The frequency P (B, C, s, θ) occurred simultaneously for the pixel position (x+Dx, y+Dy) of C.
P (B, C, s, θ)=[(x, y), (x+Dx, y+Dy) | f (x, y)=B, f (x+Dx, y+Dy)=C] } (19)
In formula (19), B, C=0,1,2 ..., 255 be grey level, Dx, Dy be respectively both horizontally and vertically on position
Setting offset, s is the step-length of grayscale image matrix, and θ is the direction that grayscale image matrix generates, take 0 °, 45 °, 90 °, 135 ° of 4 sides
To such as 4 generation directions that Fig. 5 is gray level co-occurrence matrixes.
Pass through normalization process process by formula (20).
Step 6, the characteristic statistic entropy of gray level co-occurrence matrixes is chosen.
Entropy is calculated by formula (21)
Take s=1, e1,e2,a3,a4Respectively represent 0 °, 45 °, 90 °, the entropy in 135 ° of directions.
Step 7, right if two operating conditions of rotor-support-foundation system are j (j=1 represents flawless rotor, and j=2 represents cracked rotor)
In the feature vector of i-th of IMF component of a certain operating condition be just Hji=[ei1,ei2,ei3,ei4], it is 4 dimensional vectors.
Step 8,0 ° for then seeking N number of sample under corresponding states respectively, 45 °, 90 °, the average value of the entropy in 135 ° of directions,
Corresponding states feature reference vectors are obtained, are as follows:
Step 9, acquisition to diagnostic sample several, also pass through the above process, extract feature vector Hji=[ei1,
ei2,ei3,ei4]
Step 10, the state of the feature vector of i-th of IMF of diagnostic data and i-th of IMF of j state is calculated separately
Mahalanobis distance (Mahalanobis distance) between reference feature vector, can effectively calculate unknown sample collection similarity.
Var is the variance for calculating all corresponding elements of sampling feature vectors.
Step 11, the calculating of state comprehensive distance, the synthesis of sample to be tested characteristic sequence and each state reference signal are carried out
Distance, and give corresponding weighting coefficient b1, bk, such as following formula:
dj=b1·dj1+b2·dj2+…+bk·djk (24)
Step 12, finally compare the d of sample to be tested1,d2Size, determine comprehensive distance smaller be exactly sample to be diagnosed
This corresponding state.
Beneficial effects of the present invention are further illustrated below with reference to specific example.
Acquisition has crackle and each 9 groups of flawless state, and first 6 groups are used as sample, and latter 3 groups are used as to diagnostic signal, and acquisition has
Vibration signal under crackle state and flawless state, Fig. 6 and Fig. 7 are respectively that the time-domain signal figure of flawless rotor and crackle turn
The time-domain signal figure of son, takes K=4, L=3, g=π/6, θ=0,Weighting coefficient takes
b1=0.03, b2=0.03, b3=0.03, b4=0.01.
Table 1 is system mode feature reference vectors；Table 2 is the variance from each element of sample signal extracted vector；Table 3 is
To diagnostic sample condition diagnosing result.
It can be obtained from table 3, the feature reference vectors of 3 flawless axis samples and two states calculate comprehensive distance, warp
Compare, obtaining wherein relatively short distance is respectively 1.492,1.735,1.394, corresponding with flawless Spindle Status.Equally, 3 split
The feature reference vectors of line axis sample and two states calculate comprehensive distance, and obtaining relatively short distance is respectively 1.576,1.157,
0.995, it is also corresponding with crackle Spindle Status.The experimental results showed that 6 measured signal full diagnostics successes.
In order to enhance comparison, by flawless signal and Signal of Cracks, without variation mode decomposition process, ash is directly established
It spends co-occurrence matrix and extracts feature vector, carry out mahalanobis distance judgement, distance results are calculated multiplied by coefficient 0.1.As a result such as table
4.It is connect it can be seen that No. 3 sample diagnostic errors of flawless rotor, No. 2 sample diagnostic errors of cracked rotor, and each group distance all compare
Closely, not sensitive enough to fault signature.So the present invention overcomes merely using gray level co-occurrence matrixes in rotor crack fault signal
The deficiency of processing can complete rotor crack fault diagnosis very well.
Table 1
Table 2
Table 3
Table 4
Above description is the detailed description for the present invention preferably possible embodiments, but embodiment is not limited to this hair
Bright patent claim, it is all the present invention suggested by technical spirit under completed same changes or modifications change, should all belong to
In the covered the scope of the patents of the present invention.
Claims (5)
1. a kind of rotor crack fault diagnostic method based on variation mode decomposition and gray level co-occurrence matrixes, it is characterised in that: first
The critical speed of rotor-support-foundation system is first measured, then makes rotor-support-foundation system under the operating condition of 1.5 times of critical speed of actual speed, is carried out
Following processing:
Step 1: the radial vibration on current vortex sensor and infrared electro speed probe acquisition rotor at any is respectively adopted
Signal and rotor speed signal, acquisition have N number of sample under cracked rotor and flawless rotor two states；
Step 2: collected signal { x (n) } being subjected to variation mode decomposition, i.e., K mode is sought to the vibration signal of rotor
Function uk(t), K IMF component is obtained；
Step 3: symmetrical polar image is generated to each IMF component；
Step 4: converting gray level image for symmetrical polar image；
Step 5: grayscale image generates gray level co-occurrence matrixes, extracts image texture characteristic as characteristic parameter；
Step 6: choosing the characteristic statistic entropy of gray level co-occurrence matrixes, take e1, e2, a3, a4Respectively represent 0 °, 45 °, 90 °, 135 ° of sides
To entropy；
Step 7: setting two operating conditions of rotor-support-foundation system as j, wherein j=1 represents flawless axis, and j=2 represents crackle axis, to Mr. Yu
The feature vector of i-th of IMF component of one operating condition is just Hji=[ei1, ei2, ei3, ei4], it is 4 dimensional vectors；
Step 8: and then 0 ° of N number of sample under corresponding states is asked respectively, 45 °, 90 °, the average value of the entropy in 135 ° of directions obtains
Corresponding states feature reference vectors, are as follows:
Step 9: acquisition to diagnostic sample several, also pass through the above process, extract feature vector Hji=[ei1, ei2, ei3,
ei4]
Step 10: passing through formulaCalculate separately the feature vector of i-th of IMF of diagnostic data
Mahalanobis distance between the state reference feature vector of i-th of IMF of j state；
Step 11: calculating state comprehensive distance, the comprehensive distance of sample to be tested characteristic sequence and each state reference signal, and give
Give corresponding weighting coefficient b1..., bk, calculating formula are as follows: dj=b1·dj1+b2·dj2+…+bk·djk；
Step 12: comparing the d of sample to be tested1, d2Size, determine comprehensive distance smaller is exactly corresponding to diagnostic sample
State.
2. method for diagnosing faults according to claim 1, it is characterised in that: in the step (2), variation mode decomposition
Step includes:
Step 2.1: initializationIn formula, ukTo decompose K obtained modal components, ωkFor each mode point
Corresponding center frequency is measured, ^ is the frequency domain representation using Parseval/Plancherel Fourier's equilong transformation, and λ is
Lagrange multiplier, n are the number of iterations；
Step 2.2: updatingWith
Step 2.3: update operator
Step 2.4: step 2.2~2.4 are repeated, until meet the condition of convergence,It is given to sentence
Other precision ∈ > 0, end loop export K IMF component.
3. method for diagnosing faults according to claim 2, it is characterised in that: by symmetrical polar image in the step 4
It is converted into gray level image method particularly includes: set symmetrical polar image array W, size is m × n, a row b column
Element value is A(a, b), maximum value A in symmetrical polar imagemaxIt is corresponding with tonal gradation 255, minimum value AminWith tonal gradation
0 is corresponding, and being converted into gray value by following formula is
Unit8 is 8 rounding operation symbols of no symbol, and operation result is the integer between 0~255.
4. method for diagnosing faults according to claim 1, it is characterised in that: in the step 5 method particularly includes: from ash
The pixel position (x, y) that grey level on degree figure is B sets out, and statistics is s at a distance from it, and grey level is the pixel position of C
Set the frequency P (B, C, s, θ) that (x+Dx, y+Dy) occurs simultaneously.
P (B, C, s, θ)=[(x, y), (x+Dx, y+Dy) | f (x, y)=B, f (x+Dx, y+Dy)=C] } (19)
In formula (19), B, C=0,1,2 ..., 255 be grey level, Dx, Dy be respectively both horizontally and vertically on position it is inclined
Shifting amount, s are the step-length of grayscale image matrix, and θ is the direction that grayscale image matrix generates, and take 0 °, 45 °, 90 °, and 135 ° of 4 directions,
Pass through normalization process process by formula (20)
Wherein, g (B, C) indicates that P (B, C) matrix passes through the matrix that Regularization process obtains.
5. method for diagnosing faults according to claim 1, it is characterised in that: entropy is calculated as follows in the step 6:
Take s=1, e1, e2, a3, a4Respectively represent 0 °, 45 °, 90 °, the entropy in 135 ° of directions.
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