CN104091088B - A kind of bearing fault quantitative Diagnosis method based on step struck atom storehouse MP algorithms - Google Patents

Abstract

A kind of MP algorithm bearing fault quantitative Diagnosis methods based on step struck atom storehouse.The present invention by bearing fault signal representation into succinct, sparse step struck atom linear superposition form.Step impacts response forms of the dictionary according to produced by the into and through failure of bearing fault ball, and step and shock response are got up by failure size, turn information association such as frequency and bearing size, a New type atom storehouse comprising failure size information is formed.It is iterated selection most matched atoms, updates residual signals, till stopping criterion for iteration, reconstruction signal by MP algorithm.First time discreet value is obtained by the analysis to reconstructing time domain plethysmographic signal, the fault message for screening the minimum atom of final determination deviation absolute value is carried out to estimate fault value for the second time to reconstructing atom by deviation Filtering system, the meansigma methodss for finally asking for discreet value twice are capable of achieving the countershaft quantitative Diagnosis for holding failure.

Description

A kind of bearing fault quantitative Diagnosis method based on step-struck atom storehouse MP algorithms

Technical field

The invention belongs to fault diagnosis technology field, is related to a kind of bearing fault quantitative Diagnosis method, it is more particularly to a kind of Bearing fault quantitative Diagnosis method based on step-struck atom storehouse MP algorithms.

Background technology

Bearing is the important composition part for rotating class plant equipment, and fault rate is higher.At present, bearing failure diagnosis research master In terms of the etiologic diagnosis such as the pattern recognition concentrated on by judgement that failure whether there is and fault type, but mechanical fault diagnosis are needed Realize the generation of equipment failure state, development and Evolution are disclosed by the breakthrough of qualitative investigation to quantitative study, so as to do To maintenance of equipment is really effectively instructed, production cost is saved.

In terms of quantitative Diagnosis, Chinese scholars have carried out Beneficial and have obtained certain achievement.It is serious for failure at present The assessment of degree is based primarily upon the angle and evaluation index angle of energy, including sets up according to local energy to estimate tooth root crackle The empirical model of size, realizes the equipment of Injured level vibration signal according to the proportional hazards model for introducing degeneration index Bearing fault quantitative Diagnosis are had certain effect from energy point of view and evaluation index angle by the methods such as operational reliability assessment Really, but above method is mostly that fault degree development trend is weighed, inreal judgement is out of order actual size. 2011, N.Sawalhi and R.B.Randall passed through " double impacts " phenomenon in experimental verification bearing fault time domain plethysmographic signal Presence, and impulse form differ twice, bearing ball shows as the form of step response into failure, and ball with There is shock and then show as impulse form in failure back edge, author is realized by the analysis to time interval between two Secondary Shocks The quantitative Diagnosis of bearing fault.2013, this " double impacts " phenomenon was combined by Zhao Shuanfeng et al. with EMD algorithms, same real The quantitative Diagnosis of failure are showed.It can be seen that, the quantitative Diagnosis of failure can be realized by studying " double impacts " phenomenon, and which kind of is applied Method is accurately separated the emphasis and difficult point for becoming research by this two Secondary Shocks.

The matching pursuit algorithm (Matching Pursuit, MP) that Mallat and Zhang are proposed with flexible basic function, Extraction and separation to individual features signal can be realized, therefore constructs suitable atom, bearing of the application based on MP algorithms Failure quantitative Diagnosis are a kind of new exploration and trial.But often contain substantial amounts of noise in actual signal, will certainly increase and examine Disconnected difficulty, this precision just to diagnosing propose higher requirement.

The content of the invention

In order to solve the above-mentioned technical problem in bearing fault quantitative Diagnosis, the invention provides a kind of be based on step-punching Hit the bearing fault quantitative Diagnosis method of atom MP algorithm.The vibration signal of bearing fault shows as the cycle caused by resonance Property the modulation that causes of pulse and non-homogeneous load, and with substantial amounts of background noise.In traditional bearing fault Analysis on Mechanism, For failure impact all assumes that the time for the preferable i.e. pulse active force of pulse form levels off to zero.However, this Preferable pulse is only suitable only for the minimum situation of size of rolling bearing local damage.But, with the increase of fault degree, i.e., When failure has one fixed width, the pulse that failure causes can not possibly be presented a kind of preferable pulse state, but " double impacts " shape There is certain proportionate relationship with failure size in the time interval between state, and two Secondary Shocks.Have confirmed the first Secondary Shocks Response be step response, the response of the second Secondary Shocks is shock response.In order to realize failure quantitative Diagnosis, analyze first twice The relation between time interval and failure size between impact, then constructs a step containing fault message-impact former Word bank is to match fault-signal feature during match tracing.

For achieving the above object, the technical solution used in the present invention is a kind of based on step-struck atom storehouse MP algorithms Bearing fault quantitative Diagnosis method, the method include S1 collection bearing vibration signals；S2 is carried out based on rank to bearing vibration signal Jump-struck atom storehouse MP algorithms decompose and reconstruction signal；S3 carries out failure to reconstruct time domain plethysmographic signal process and estimates, and extracts each Individual reconstruct atom carries out deviation screening and carries out failure quadratic estimate, and estimated value averaged obtains final fault value twice.

Ball the time required to rolling across failure is

Wherein, l₀Represent failure size (mm), D₀Represent bearing outside diameter (mm), D₀=D_p+ d, is shown in Fig. 3, f_cRepresent retainer Turn frequency (Hz),f_rTurning frequently (Hz) for axle, α is pressure angle；

Therefore, the time that ball rolls across needed for failure is

And when fault diameter is less than ball diameter, when ball and failure back edge are collided, now ball center institute Jing The distance crossed is exactly the half of failure size, sees Fig. 3, therefore, the time interval between two Secondary Shocks is

Therefore, between failure size and two Secondary Shocks, the relational expression of time interval is

Two Secondary Shocks are respectively step response and shock response, the i.e. moment of step response generation when shock response occurs The front Δ t times carved, the time for impacting moment generation are u, therefore, the moment that step response occurs is u- Δ t.

The expression formula of shock response is

The expression formula of step response is

Therefore, the basic function model in step-struck atom storehouse is：

X=ax_imp+x_step

Wherein, u be impact occur moment (s), τ be system damping coefficient (s), f_nFor system frequency (Hz), a is Impact composition and step multicomponent energy ratio.Parameters in basic function are carried out with discretization assignment, atom is defined, D (u, τ, f_n, l₀)={ g_i, i=1,2,3 ..., m ... }, wherein, D (u, τ, f_n, l₀) for step-struck atom storehouse, g_iFor atom, ‖ g_i‖ =1, it is the atom with unit energy Jing after normalized, m is atom number.

Comprised the following steps based on the bearing fault quantitative Diagnosis method of step-struck atom storehouse MP algorithms：

S1 initializes residual error.Gear-box is measured using acceleration transducer, obtain vibration acceleration signal conduct Signal f to be decomposed is assigned to residual signals by signal f to be analyzed, obtains initial residual signals R₀。

S2 most matched atoms are chosen.As following formula carries out the selection of most matched atoms, then the most matched atoms of kth iteration are g_0j, wherein j=1,2,3 ..., K, K are iterationses.

|<R_k-1, g_0j>|=sup |<R_k-1, g_i>|

S3 updates residual signals.Residual signals deduct projection of the residual signals in most matched atoms, you can obtain new Residual signals.

Projection coefficient is,

c_j=<R_j, g_0j>

New residual signals are,

R_j+1=R_j-c_jg_0j

S4 iteration ends.Need to choose suitable stopping criterion for iteration, such as iterationses, residual signals energy according to different Amount decay, residual error ratio threshold value.Then matching process terminates to meet end condition, otherwise circulates execution step S2～S3.

(2.5) signal reconstruction.By the matching pursuit linear superposition of K signal, approximate reconstruction signal is obtained：

(2.6) fault value is estimated.By reconstruction signal time domain waveform obtain that step response and shock response occur when Carve u₁、u₂, and its time interval of delta t ' is asked for, fault value l ' is estimated according to formula (4).

Δ t '=u₂-u₁

S7 atoms are screened.Ask for the failure size of most matched atoms in each iterative process and estimate between fault value l ' Absolute value of the bias, and choose the minimum atom of absolute value of the bias, records failure size which reflects as secondary discreet value l′_g：

|σ|_min=min ‖ l₀-l′‖

S8 quantitative Diagnosis.Final failure size l is estimates failure with the meansigma methodss of secondary discreet value：

Compared with present technology, the present invention has the advantages that.

Bearing fault vibration signal successive iteration is resolved into the present invention K item atoms based on step-struck atom storehouse Linear combination.Step-struck atom storehouse introduces failure size, turns the information such as frequency and bearing size, by each to its basic function Individual parameter carries out discretization assignment construction, and truly simulates the process that ball entered and rolled across failure, by two Secondary Shocks Time interval realizes step response and shock response contact, and each atom carries the operation that fault message is easy to quantitative Diagnosis. During each Breaking Recurrently of signal, a most matched atoms, signal projection, signal are chosen from step-struck atom storehouse Deduct projection residual signals are formed for decomposition next time, finally by each matched atoms linear combination reconstruction signal.Quantitative Diagnosis The step of be, after MP algorithms, analysis to be carried out in its time domain to reconstruction signal first and estimates failure size, by deviation Filtering system, obtains the minimum atom of absolute value of the bias, carries out the secondary of failure by its own information for carrying and estimate, finally Discreet value averaged twice is realized into the quantitative Diagnosis of failure.

Description of the drawings

Fig. 1 is the bearing fault quantitative Diagnosis method flow diagram based on step-struck atom storehouse MP algorithms of the present invention.

Fig. 2 is the bearing fault quantitative Diagnosis method overall flow based on step-struck atom storehouse MP algorithms of the present invention Figure.

Fig. 3 be the outer ring simulated in the present invention exist 1.2mm failures bearing vibration signal dye make an uproar after time domain waveform and Spectrogram.

Fig. 4 is reconstruction signal waveform and its frequency spectrum in the present invention (containing estimating).

Specific embodiment

The invention will be further described with reference to the accompanying drawings and detailed description.

Fig. 1 is the bearing fault quantitative Diagnosis method flow diagram based on step-struck atom storehouse MP algorithms of the present invention.Under Face is with reference to flow chart to being carried out specifically based on the bearing fault quantitative Diagnosis Method And Principle of step-struck atom storehouse MP algorithms It is bright.

(1) gear-box is measured using acceleration vibrating sensor, vibration acceleration signal is obtained as to be analyzed Signal f, sampling length are set to 2 integer power, according to bearing rotating speed and number of gear teeth setting sample frequency；

(2) vibration signal of bearing fault shows as the tune that the recurrent pulses caused by resonance and non-homogeneous load cause System, but this pulse is not preferable pulse situation, but have the presence of " double impacts " phenomenon, and the response of the first Secondary Shocks For step response, the response of the second Secondary Shocks is shock response.In order to realize failure quantitative Diagnosis, analyze first two Secondary Shocks it Between time interval and failure size between relation, then construct step containing fault message-struck atom storehouse and use So that fault-signal feature is matched during match tracing.

Between failure size and two Secondary Shocks, the relational expression of time interval is

Wherein, l₀Represent failure size (mm), D₀Represent bearing outside diameter (mm), D₀=D_p+ d, is shown in Fig. 3, f_cRepresent retainer Turn frequency (Hz),f_rTurning frequently (Hz) for axle, α is pressure angle.

Two Secondary Shocks are respectively step response and shock response, the i.e. moment of step response generation when shock response occurs The front Δ t times carved, the time for impacting moment generation are u, therefore, the moment that step response occurs is u- Δ t.

The expression formula of shock response is

The expression formula of step response is

Therefore, the basic function model in step-struck atom storehouse is：

X=ax_imp+x_step

Wherein, u be impact occur moment (s), τ be system damping coefficient (s), f_nFor system frequency (Hz), a is Impact composition and step multicomponent energy ratio.Parameters in basic function are carried out with discretization assignment, atom is defined, D (u, τ, f_n, l₀)={ g_i, i=1,2,3 ..., m ... }, wherein, D (u, τ, f_n, l₀) for step-struck atom storehouse, g_iFor atom, ‖ g_i‖ =1, it is the atom with unit energy Jing after normalized, m is atom number.

(3) it is analysed to signal and is assigned to initial residual signals R₀=f；

(4) residual signals carry out the selection of most matched atoms in atom, then the most matched atoms of kth iteration are g_0j, wherein j=1,2,3 ..., K, K are iterationses.

|<R_k-1, g_0j>|=sup |<R_k-1, g_i>|

(5) seek residual signals kth iterative projection coefficient c on step-impact dictionary_j, it is residual that projection coefficient passes through calculating The inner product realization of difference signal and matched atoms, i.e.,：c_j=<R_j, g_0j>, residual signals deduct residual signals in most matched atoms Projection, you can obtain new residual signals R_j+1=R_j-c_jg_0j。

(6) check whether to meet stopping criterion for iteration (such as：Iteration reaches certain number of times, and residual signals energy is little to certain Threshold value, residual signals and initial signal energy ratio are little to certain threshold value etc.).If it is satisfied, going to step (7), step is otherwise returned Suddenly (4)；

(7) reconstruction signal, and time-domain analyses are carried out to reconstruction signal, obtain failure discreet value l '.

(8) by deviation Filtering system, the minimum atom of absolute value of the bias is obtained, its failure size for reflecting is recorded As secondary discreet value l '_g。

(9) meansigma methodss of discreet value twice are asked for, you can realize failure quantitative Diagnosis, obtains final failure size l.

Fig. 2 is its overall flow figure of gear failure diagnosing method proposed by the present invention.

Fig. 3 simulates the bearing vibration signal time domain waveform and spectrogram that the outer ring after a dye is made an uproar has 1.2mm failures, adopts Sample frequency is 65536Hz, and sampling number is 2048 points.As can be seen that the first Secondary Shocks are submerged in noise.Using based on rank The bearing fault quantitative Diagnosis method handling failure signal of jump-struck atom storehouse MP algorithms, it is possible to achieve the reconstruct of signal, and The quantitative Diagnosis for finally realizing failure by estimating 1.152mm and 1.19mm twice are 1.171mm, as a result more accurately, and The accuracy for significantly improving judgement is estimated twice.

Fig. 4 be the bearing fault quantitative Diagnosis reconstruction signal time domain waveform based on step-struck atom storehouse MP algorithms and its Spectrogram (containing estimating).

Claims (3)

1. a kind of bearing fault quantitative Diagnosis method based on step-struck atom storehouse MP algorithms, it is characterised in that：

In traditional bearing fault Analysis on Mechanism, for failure impact is all assumed that as preferable pulse form i.e. pulse The time of active force levels off to zero；However, the size that this preferable pulse is only suitable only for rolling bearing local damage is minimum Situation；But, with the increase of fault degree, i.e., when failure has one fixed width, the pulse that failure causes can not possibly be presented one Preferable pulse state is planted, but the time interval of " double impacts " between state, and two Secondary Shocks has one with failure size Fixed proportionate relationship；The response for having confirmed the first Secondary Shocks is step response, and the response of the second Secondary Shocks is shock response；For Realize failure quantitative Diagnosis, analyze the relation between the time interval between two Secondary Shocks and failure size first, then structure The step containing a fault message-struck atom storehouse is made fault-signal feature is matched during match tracing；

Ball the time required to rolling across failure is

${\mathrm{\&Delta;t}}_0=\frac{l_0}{{\mathrm{\&pi;D}}_0{f}_c}$

Wherein, l₀Represent failure size, D₀Represent bearing outside diameter, D₀=D_p+ d, f_cRepresent that retainer turns frequency,f_rTurn frequency for axle, α is pressure angle, D_pFor ball centre of sphere running track diameter, d is ball Diameter；

Therefore, the time that ball rolls across needed for failure is

${\mathrm{\&Delta;t}}_0=\frac{l_0}{\mathrm{\&pi;}(D_p+d)}\frac{2}{f_r(1-\frac{d}{D_p})}=\frac{2l_0{D}_p}{{\mathrm{\&pi;f}}_r({D_p}^2-d^2)}$

And when fault diameter is less than ball diameter, when ball is collided with failure back edge, now ball center is passed through Apart from the half of exactly failure size, therefore, the time interval between two Secondary Shocks is

$\mathrm{\&Delta;}t=\frac{{\mathrm{\&Delta;t}}_0}{2}$

Therefore, between failure size and two Secondary Shocks, the relational expression of time interval is

$l_0=\frac{{\mathrm{\&pi;f}}_r({D_p}^2-d^2)}{D_p}\mathrm{\&Delta;}t$

Two Secondary Shocks are respectively step response and shock response, i.e. the moment of step response generation occurs the moment in shock response Front Δ t times, the moment for impacting generation are u, therefore, the moment that step response occurs is u- Δ t；

The expression formula of shock response is

$x_{imp}=e^{\frac{-(t-u)}{\mathrm{\&tau;}}}\sin \left(2{\mathrm{\&pi;f}}_{n}t\right)$

The expression formula of step response is

$x_{step}=(-\cos (2\mathrm{\&pi;}\&CenterDot;\left(\frac{f_n}{6}\right)\&CenterDot;t)\&CenterDot;e^{\frac{-(t-u-\mathrm{\&Delta;}t)}{s\mathrm{\&tau;}}})+e^{\frac{-(t-u)}{s\mathrm{\&tau;}}}$

Therefore, the basic function model in step-struck atom storehouse is：

X=ax_imp+x_step

Wherein, u be impact occur moment, τ be system damping coefficient, f_nFor system frequency, a is impact composition and step Multicomponent energy ratio；Parameters in basic function are carried out with discretization assignment, atom, D (u, τ, f is defined_n, l₀)={ g_i, i=1, 2,3 ..., m ... }, wherein, D (u, τ, f_n, l₀) for step-struck atom storehouse, g_iFor atom, | | g_i| |=1, it is Jing normalizings Change has the atom of unit energy after processing, m is atom number；

Step-struck atom storehouse introduces failure size, turns the information such as frequency and bearing size, by its basic function parameters Carry out discretization assignment construction, and truly simulate the process that ball entered and rolled across failure, by twice between the attack time Every step response and shock response contact is realized, each atom carries the operation that fault message is easy to quantitative Diagnosis.

2. a kind of bearing fault quantitative Diagnosis method based on step-struck atom storehouse MP algorithms according to claim 1, It is characterized in that：The method includes step in detail below：

(1) initialize residual error；Gear-box is measured using acceleration transducer, vibration acceleration signal is obtained as treating point Signal f to be decomposed is assigned to residual signals, obtains initial residual signals R by analysis signal f₀；

(2) most matched atoms are chosen；As following formula carries out the selection of most matched atoms, then the most matched atoms of kth iteration are g_0j, Wherein g₀Represent most matched atoms, j=1,2,3 ..., K, K be iterationses；

|<R_k-1, g_0j>|=sup |<R_k-1, g_i>|

(3) residual signals are updated；Residual signals deduct projection of the residual signals in most matched atoms, you can obtain new residual error Signal；

Projection coefficient is,

c_j=<R_j, g_0j>

New residual signals are,

R_j+1=R_j-c_jg_0j

(4) iteration ends；According to the stopping criterion for iteration that different needs can be chosen, such as iterationses, residual signals energy attenuation, Residual error ratio threshold value；Then matching process terminates to meet end condition, otherwise circulates execution step S2～S3；

(5) signal reconstruction；By the matching pursuit linear superposition of K signal, approximate reconstruction signal is obtained：

$f=\underset{j=1}{\overset{K}{\&Sigma;}}{c}_j{g}_{0j}$

(6) fault value is estimated；The moment u that step response and shock response occur is obtained by reconstruction signal time domain waveform₁、u₂, And its time interval of delta t ' is asked for, fault value l ' is estimated according to following formula；

Δ t '=u₂-u₁

$l^{\&prime;}=\frac{{\mathrm{\&pi;f}}_r({D_p}^2-d^2)}{D_p}{\mathrm{\&Delta;t}}^{\&prime;}$

(7) atom screening；Ask for the failure size of most matched atoms in each iterative process and estimate inclined between fault value l ' Difference absolute value, and choose the minimum atom of absolute value of the bias, records failure size which reflects as secondary discreet value l ' g：

|σ|_min=min | | l₀-l′||

(8) quantitative Diagnosis；Final failure size l is estimates failure with the meansigma methodss of secondary discreet value

$l=\frac{1}{2}(l^{\&prime;}+l_g^{\&prime;}).$

3. a kind of bearing fault quantitative Diagnosis method based on step-struck atom storehouse MP algorithms according to claim 1, It is characterized in that：

(1) gear-box is measured using acceleration vibrating sensor, vibration acceleration signal is obtained as signal to be analyzed F, sampling length are set to 2 integer power, according to bearing rotating speed and number of gear teeth setting sample frequency；

(2) vibration signal of bearing fault shows as the modulation that the recurrent pulses caused by resonance and non-homogeneous load cause, But this pulse is not preferable pulse situation, but there is the presence of " double impacts " phenomenon, and the response of the first Secondary Shocks is Step response, the response of the second Secondary Shocks is shock response；In order to realize failure quantitative Diagnosis, analyzed between two Secondary Shocks first Time interval and failure size between relation, then construct the step containing a fault message-struck atom storehouse to Fault-signal feature is matched during match tracing；

Between failure size and two Secondary Shocks, the relational expression of time interval is

$l_0=\frac{{\mathrm{\&pi;f}}_r({D_p}^2-d^2)}{D_p}\mathrm{\&Delta;}t$

Wherein, l₀Represent failure size, D₀Represent bearing outside diameter, D₀=D_p+ d, f_cRepresent that retainer turns frequency,f_rTurn frequency for axle, α is pressure angle, D_pFor ball centre of sphere running track diameter, d is ball Diameter；

Two Secondary Shocks are respectively step response and shock response, i.e. the moment of step response generation occurs the moment in shock response Front Δ t times, the moment for impacting generation are u, therefore, the moment that step response occurs is u- Δ t；

The expression formula of shock response is

$x_{imp}=e^{\frac{-(t-u)}{\mathrm{\&tau;}}}\sin \left(2{\mathrm{\&pi;f}}_{n}t\right)$

The expression formula of step response is

$x_{step}=(-\cos (2\mathrm{\&pi;}\&CenterDot;\left(\frac{f_n}{6}\right)\&CenterDot;t)\&CenterDot;e^{\frac{-(t-u-\mathrm{\&Delta;}t)}{s\mathrm{\&tau;}}})+e^{\frac{-(t-u)}{s\mathrm{\&tau;}}}$

Therefore, the basic function model in step-struck atom storehouse is：

X=ax_impTen x_step

Wherein, u be impact occur moment, τ be system damping coefficient, f_nFor system frequency, a is impact composition and step Multicomponent energy ratio；Parameters in basic function are carried out with discretization assignment, atom, D (u, τ, f is defined_n, l₀)={ g_i, i=1, 2,3 ..., m ... }, wherein, D (u, τ, f_n, l₀) for step-struck atom storehouse, g_iFor atom, | | g_i| |=1, it is Jing normalizings Change has the atom of unit energy after processing, m is atom number；

(3) it is analysed to signal and is assigned to initial residual signals R₀=f；

(4) residual signals carry out the selection of most matched atoms in atom, then the most matched atoms of kth iteration are g_0j, its Middle j=1,2,3 ..., K, K be iterationses；

|<R_k-1, g_0j>|=sup |<R_k-1, g_i>|

(5) seek residual signals kth iterative projection coefficient c on step-impact dictionary_j, projection coefficient is by calculating residual signals Realize with the inner product of matched atoms, i.e.,：c_j=<R_j, g_0j>, residual signals deduct projection of the residual signals in most matched atoms, New residual signals R is obtained_j+1=R_j-c_jg_0j；

(6) check whether to meet stopping criterion for iteration, such as：Iteration reaches certain number of times, and residual signals energy is little to certain threshold value, Residual signals are little to certain threshold value with initial signal energy ratio；If it is satisfied, go to step (7), otherwise return to step (4)；

(7) reconstruction signal, and time-domain analyses are carried out to reconstruction signal, obtain failure discreet value l '；

(8) by deviation Filtering system, the minimum atom of absolute value of the bias is obtained, its failure size conduct for reflecting is recorded Secondary discreet value l '_g；

(9) meansigma methodss of discreet value twice are asked for, you can realize failure quantitative Diagnosis, obtains final failure size l.