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

Abstract

A quantitative diagnosis method of bearing fault based on MP algorithm based on step-impact atomic library. The invention expresses the bearing fault signal in the form of simple and sparse step-impact atomic linear superposition. The step-shock dictionary correlates the step and shock responses through fault size, rotation frequency, bearing size and other information according to the response form of the bearing fault ball entering and passing through the fault, forming a new atomic library containing fault size information. The MP algorithm is used to iteratively select the most matching atom, update the residual signal, and reconstruct the signal until the iteration termination condition. The first estimated value is obtained by analyzing the time domain waveform of the reconstructed signal, and the reconstructed atoms are screened through the deviation screening mechanism, and finally the fault information of the atom with the smallest absolute value of deviation is determined as the second estimated fault value, and finally calculated The quantitative diagnosis of bearing faults can be realized by taking the average value of the two estimated values.

Description

A Quantitative Diagnosis Method of Bearing Fault Based on Step-shock Atomic Library MP Algorithm

technical field

The invention belongs to the technical field of fault diagnosis, and relates to a bearing fault quantitative diagnosis method, in particular to a bearing fault quantitative diagnosis method based on a step-impact atomic library MP algorithm.

Background technique

Bearings are important components of rotating machinery and equipment, and have a high failure rate. At present, the research on bearing fault diagnosis mainly focuses on the qualitative diagnosis such as the judgment of the fault and the pattern recognition of the fault type. Evolution law, so as to truly effectively guide equipment maintenance and save production costs.

Scholars at home and abroad have made useful attempts in quantitative diagnosis and achieved certain results. At present, the evaluation of fault severity is mainly based on the angle of energy and evaluation index, including the establishment of an empirical model based on local energy to estimate the size of tooth root cracks, and the operation of equipment with vibration signals of different damage degrees based on the proportional failure rate model that introduces degradation indicators. Methods such as reliability evaluation have a certain effect on the quantitative diagnosis of bearing faults from the perspective of energy and evaluation indicators, but the above methods mostly measure the development trend of the fault degree, and do not really judge the actual size of the fault. In 2011, N.Sawalhi and R.B.Randall verified the existence of the "double shock" phenomenon in the time domain waveform of the bearing fault signal through experiments, and the forms of the two shocks were not the same, and the bearing ball entered the fault as a step response, while The collision between the ball and the rear edge of the fault is in the form of impact. The author realizes the quantitative diagnosis of bearing faults by analyzing the time interval between the two impacts. In 2013, Zhao Shuanfeng and others combined this "double shock" phenomenon with the EMD algorithm, and also realized the quantitative diagnosis of faults. It can be seen that the quantitative diagnosis of faults can be realized by studying the "double impact" phenomenon, and the method to be used to accurately separate the two impacts has become the focus and difficulty of the research.

The matching pursuit algorithm (Matching Pursuit, MP) proposed by Mallat and Zhang has a flexible basis function, which can realize the extraction and separation of the corresponding characteristic signals, so constructing a suitable atomic library and applying the MP algorithm to the quantitative diagnosis of bearing faults is a Explore and try new things. However, the actual signal often contains a lot of noise, which will inevitably increase the difficulty of diagnosis, which puts forward higher requirements for the accuracy of diagnosis.

Contents of the invention

In order to solve the above-mentioned technical problems in the quantitative diagnosis of bearing faults, the present invention provides a method for quantitative diagnosis of bearing faults based on the step-impact atomic library MP algorithm. The vibration signals of bearing faults appear as periodic pulses caused by resonance and modulated by non-uniform loads, accompanied by a large amount of background noise. In the traditional analysis of bearing failure mechanism, the fault impact is assumed to be an ideal single-pulse form, that is, the time of single-pulse force approaches zero. However, this ideal single pulse is only suitable for the case where the size of the local damage of the rolling bearing is extremely small. However, as the degree of fault increases, that is, when the fault has a certain width, the pulse caused by the fault cannot present an ideal single pulse state, but a "double shock" state, and the time interval between two shocks is related to the fault size There is a certain proportional relationship. It has been confirmed that the response to the first shock is a step response and the response to the second shock is an impulse response. In order to achieve quantitative fault diagnosis, the relationship between the time interval between two shocks and the fault size is firstly analyzed, and then a step-shock atomic library containing fault information is constructed to match fault signal characteristics in the matching pursuit process.

In order to achieve the above object, the technical solution adopted by the present invention is a method for quantitative diagnosis of bearing faults based on the MP algorithm of the step-shock atomic library. The method includes S1 collecting the vibration signal of the bearing; The atomic library MP algorithm decomposes and reconstructs the signal; S3 performs fault prediction on the time-domain waveform processing of the reconstructed signal, extracts each reconstructed atom for deviation screening to perform secondary fault estimation, and calculates the average value of the two estimated values to obtain the final fault value .

The time required for the ball to roll over the fault is

Among them, l ₀ represents the fault size (mm), D ₀ represents the outer diameter of the bearing (mm), D ₀ =D _p +d, see Figure 3, f _c represents the cage rotation frequency (Hz), f _r is the rotational frequency (Hz) of the shaft, and α is the pressure angle;

Therefore, the time required for the ball to roll over the fault is

And when the diameter of the fault is smaller than the diameter of the ball, when the ball collides with the rear edge of the fault, the distance passed by the center of the ball is exactly half of the fault size, as shown in Figure 3. Therefore, the time interval between two impacts is

Therefore, the relationship between the magnitude of the fault and the time interval between two shocks is

The two shocks are step response and impulse response respectively, that is, the moment when the step response occurs is Δt before the moment when the impulse response occurs, and the time when the impact moment occurs is u, so the moment when the step response occurs is u-Δt.

The expression of the impulse response is

The expression for the step response is

Therefore, the basis function model of the step-shock atomic library is:

x＝a·x _imp +x _step

Among them, u is the moment when the impact occurs (s), τ is the system damping coefficient (s), f _n is the system natural frequency (Hz), and a is the energy ratio of the impact component to the step component. Carry out discretization assignment to each parameter in the basis function, define the atomic library, D(u, τ, f _n , l ₀ )={g _i , i=1, 2, 3,..., m,...}, where, D (u, τ, f _n , l ₀ ) is the step-impact atomic library, g _i is the atom, ‖g _i ‖=1, is the atom with unit energy after normalization, m is the number of atoms.

The quantitative diagnosis method of bearing fault based on step-impact atomic library MP algorithm includes the following steps:

S1 initializes the residual. The acceleration sensor is used to measure the gearbox, and the vibration acceleration signal is obtained as the signal f to be analyzed, and the signal f to be decomposed is assigned to the residual signal to obtain the initial residual signal R ₀ .

S2 is the best match for atom selection. The best matching atom is selected according to the following formula, then the best matching atom of the Kth iteration is g _0j , where j=1, 2, 3, . . . , K, K is the number of iterations.

|<R _k-1 ，g _0j >|＝sup|<R _k-1 ，g _i >|

S3 updates the residual signal. The residual signal subtracts the projection of the residual signal on the best matching atom to obtain a new residual signal.

The projection coefficient is,

c _j =<R _j ,g _0j >

The new residual signal is,

R _j+1 ＝R _j -c _j g _0j

S4 iteration terminates. Select appropriate iteration termination conditions according to different needs, such as the number of iterations, residual signal energy attenuation, and residual ratio threshold. If the termination condition is met, the matching process ends; otherwise, steps S2-S3 are executed in a loop.

(2.5) Signal reconstruction. Linearly superimpose the matching projections of K signals to obtain an approximate reconstructed signal:

(2.6) Fault value estimation. The moment u ₁ and u ₂ of the step response and the impulse response are obtained by reconstructing the time domain waveform of the signal, and the time interval Δt' is calculated, and the fault value l' is estimated according to the formula (4).

Δt'=u ₂ -u ₁

S7 atomic screening. Calculate the absolute value of the deviation between the fault size of the best matching atom and the estimated fault value l′ in each iteration, and select the atom with the smallest absolute value of the deviation, and record the fault size reflected by it as the secondary estimated value l ' _g :

|σ| _min ＝min‖l ₀ -l′‖

S8 Quantitative diagnosis. The final fault size l is the average value of the estimated fault and the second estimated value:

Compared with the prior art, the present invention has the following beneficial effects.

The invention iteratively decomposes the bearing fault vibration signal into a linear combination of K-item atoms based on the step-shock atomic library. The step-shock atomic library introduces information such as the size of the fault, the rotation frequency, and the size of the bearing, and constructs it by discretely assigning values to each parameter of its basis function, and truly simulates the process of the ball entering and rolling over the fault. Realize the connection between step response and impulse response, and each atom carries fault information to facilitate the operation of quantitative diagnosis. In each iterative decomposition process of the signal, a best matching atom is selected from the step-shock atomic library, the signal is projected, the signal is subtracted from the projection to form a residual signal for the next decomposition, and finally the matching atoms are linearly combined to reconstruct the signal . The step of quantitative diagnosis is to analyze the reconstructed signal in its time domain to estimate the size of the fault after the MP algorithm, and then obtain the atom with the smallest absolute value of the deviation through the deviation screening mechanism, and use the information carried by itself to diagnose the fault. The second estimate, and finally calculate the average value of the two estimated values to realize the quantitative diagnosis of the fault.

Description of drawings

Fig. 1 is a flow chart of the bearing fault quantitative diagnosis method based on the step-shock atomic library MP algorithm of the present invention.

Fig. 2 is an overall flowchart of the bearing fault quantitative diagnosis method based on the step-impact atomic library MP algorithm of the present invention.

Fig. 3 is the time-domain waveform and frequency spectrum diagram of the simulated bearing vibration signal with a 1.2mm fault in the outer ring of the present invention after being contaminated with noise.

Fig. 4 is the reconstructed signal waveform and its frequency spectrum (including estimation) in the present invention.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Fig. 1 is a flow chart of the bearing fault quantitative diagnosis method based on the step-shock atomic library MP algorithm of the present invention. The principle of the bearing fault quantitative diagnosis method based on the step-impact atomic library MP algorithm is described in detail below in conjunction with the flow chart.

(1) Utilize the acceleration vibration sensor to measure the gear box, obtain the vibration acceleration signal as the signal f to be analyzed, the sampling length is set as an integer power of 2, and the sampling frequency is set according to the bearing speed and the number of gear teeth;

(2) The vibration signal of the bearing fault is manifested by periodic pulses caused by resonance and modulation caused by non-uniform loads, but this pulse is not an ideal pulse situation, but there is a "double shock" phenomenon, and for the first time The response to the shock is a step response, and the response to the second shock is an impulse response. In order to achieve quantitative fault diagnosis, the relationship between the time interval between two shocks and the fault size is firstly analyzed, and then a step-shock atomic library containing fault information is constructed to match fault signal characteristics in the matching pursuit process.

The relationship between the size of the fault and the time interval between two shocks is

Among them, l ₀ represents the fault size (mm), D ₀ represents the outer diameter of the bearing (mm), D ₀ =D _p +d, see Figure 3, f _c represents the cage rotation frequency (Hz), f _r is the rotational frequency (Hz) of the shaft, and α is the pressure angle.

The two shocks are step response and impulse response respectively, that is, the moment when the step response occurs is Δt before the moment when the impulse response occurs, and the time when the impact moment occurs is u, so the moment when the step response occurs is u-Δt.

The expression of the impulse response is

The expression for the step response is

Therefore, the basis function model of the step-shock atomic library is:

x＝a·x _imp +x _step

Among them, u is the moment when the impact occurs (s), τ is the system damping coefficient (s), f _n is the system natural frequency (Hz), and a is the energy ratio of the impact component to the step component. Carry out discretization assignment to each parameter in the basis function, define the atomic library, D(u, τ, f _n , l ₀ )={g _i , i=1, 2, 3,..., m,...}, where, D (u, τ, f _n , l ₀ ) is the step-impact atomic library, g _i is the atom, ‖g _i ‖=1, is the atom with unit energy after normalization, m is the number of atoms.

(3) Assign the signal to be analyzed to the initial residual signal R ₀ =f;

(4) The residual signal selects the most matching atom in the atom library, then the best matching atom of the Kth iteration is g _0j , where j=1, 2, 3, ..., K, K is the number of iterations.

|<R _k-1 ，g _0j >|＝sup|<R _k-1 ，g _i >|

(5) Find the projection coefficient c _j of the Kth iteration of the residual signal on the step-shock dictionary. The projection coefficient is realized by calculating the inner product of the residual signal and the matching atom, namely: c _j =<R _j , g _0j > , the residual signal subtracts the projection of the residual signal on the best matching atom to obtain a new residual signal R _j+1 =R _j -c _j g _0j .

(6) Check whether the iteration termination condition is satisfied (for example: the iteration reaches a certain number of times, the energy of the residual signal is small to a certain threshold, the ratio of the energy of the residual signal to the initial signal is small to a certain threshold, etc.). If satisfied, go to step (7), otherwise return to step (4);

(7) Reconstruct the signal, and analyze the reconstructed signal in time domain to obtain the fault prediction value l'.

(8) Obtain the atom with the smallest absolute value of deviation through the deviation screening mechanism, and record the size of the fault reflected by it as the secondary estimated value l′ _g .

(9) By calculating the average value of the two estimated values, the fault quantitative diagnosis can be realized, and the final fault size l can be obtained.

Fig. 2 is the overall flowchart of the gear fault diagnosis method proposed by the present invention.

Figure 3 simulates the time-domain waveform and frequency spectrum of a bearing vibration signal with a 1.2mm fault in the outer ring after the noise contamination, the sampling frequency is 65536Hz, and the number of sampling points is 2048. It can be seen that the first impact is drowned in the noise. Using the bearing fault quantitative diagnosis method based on the step-impact atomic library MP algorithm to process the fault signal, the signal can be reconstructed, and the quantitative diagnosis of the fault is 1.171mm after two estimates of 1.152mm and 1.19mm. The result is relatively Accurate, and the two estimates significantly improved the accuracy of judgment.

Fig. 4 is the time-domain waveform and its frequency spectrum (including estimation) of the reconstructed signal for quantitative diagnosis of bearing faults based on the MP algorithm of the step-shock atomic library.

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.