CN104156591B - Markov fault trend prediction method - Google Patents

Abstract

The invention relates to a Markov fault trend prediction method. The method comprises the steps that (1) a rotor experiment table is used for simulating the normal running state of rotary mechanical equipment, and vibration signals generated in the normal running state are collected; (2) the rotor experiment table is used for simulating the light fault degree, the medium fault degree and the heavy fault degree of faults of the rotary mechanical equipment, and vibration signals generated in the three kinds of faults are collected; (3) a 1.5-dimension spectrum of each group of the vibration signals is calculated; (4) the average value of frequency band energy of the 1.5-dimension spectrums of the vibration signals is calculated; (5) frequency band energy intervals are obtained, and a state sequence and a state space are marked; (6) the vibration signals of the actual rotary mechanical equipment are collected, and the step (3) and the step (4) are executed to obtain the average value of the frequency band energy of the 1.5-dimension spectrums of all groups of the vibration signals, and the state sequence of the actual rotary mechanical equipment is obtained; (7) the Markov chain is used for conducting trend prediction on the state of the actual rotary mechanical equipment. The Markov fault trend prediction method can be widely applied to rotary mechanical fault trend prediction.

Description

A kind of markov failure trend prediction method

Technical field

The present invention relates to a kind of rotating machinery fault trend forecasting method, especially with regard to a kind of based on " 1.5 dimension spectrum frequency bands The markov failure trend prediction method of average energy value ".

Background technology

The safe and stable operation of rotating machinery has material impact to economy and society, is protected using scientific and effective method The safe and stable operation of barrier equipment has positive meaning.Rotating machinery is deteriorated by normal operating condition has one for malfunction Individual development and change process, if effective trend prediction can be carried out using rational Forecasting Methodology to its malfunction, is conducive to Implement advanced anticipatory maintenance and actively keep in repair, it is to avoid the generation of accident, reduce economic loss.

Content of the invention

For the problems referred to above, it is an object of the invention to provide a kind of markov failure trend prediction method, the method energy Effectively the development and change situation of rotating machinery fault is predicted, improves the accuracy of failure trend prediction.

For achieving the above object, the present invention takes technical scheme below：A kind of markov failure trend prediction method, should Method is based on 1.5 dimension spectrum frequency band energy averages and realizes, and it comprises the following steps：(1) rotor testbed is utilized to simulate rotating machinery Equipment normal operating condition, gathers rotor testbed vibration signal under normal operating conditions using available data collecting device x_w(n)={ x₁,...,x_N, wherein, N represents every group of data amount check, and w represents data group, w=1, represents normal operating condition； (2) rotor testbed is utilized to simulate minor failure degree, moderate fault degree and the severe fault journey of rotating machinery fault Three kinds of fault degrees of degree, and gather vibration signal x under three kinds of faults for the rotor testbed using available data collecting device_w (n)={ x₁,...,x_N, wherein, N represents every group of data amount check；W=2,3,4 represent data group, and w=2 represents minor failure Level state, w=3 represents moderate fault degree state, and w=4 represents severe fault degree state；(3) all vibration letters are calculated Number x_w1.5 dimension spectrums of every group of vibration signal in (n)；(4) 1.5 dimension spectrum frequency band energy averages of each group vibration signal are calculated

In formula, S_w,3x(ω_r) tie up spectrum for the 1.5 of vibration signal；ω_rRepresent frequency, r=1,2 ..., N, N are positive integer； (5) obtain frequency band energy interval：According to 1.5 dimension spectrum frequency band energy averagesThree kinds of fault journeys to rotating machinery fault Degree is quantified, and obtains the frequency band energy interval dividing malfunction：Frequency band energy average numerical value is in intervalState It is categorized as normal operating condition, be designated as state 1；Frequency band energy average numerical value is in intervalState classification be slight Malfunction, is designated as malfunction 2；Frequency band energy average numerical value is in intervalState classification be moderate fault shape State, is designated as malfunction 3；Frequency band energy average numerical value is in intervalState classification be severe malfunction, note For malfunction 4；Frequency band energy average numerical value is in intervalState classification be collapse state, be designated as malfunction 5；Remember that status switch is：{S₁,S₂,...,S_n, n is state number, is positive integer；State space E=1,2 ..., 5 }；(6) Gather the vibration signal of actual rotating machinery, this vibration signal is carried out with step (3) to the operation of step (4), obtain each 1.5 dimension spectrum frequency band energy averages of group vibration signal, the frequency band energy being given in conjunction with step (5) is interval, obtains actual whirler The status switch of tool equipment：{S₁,S₂,...,S_n}；(7) using Markov chain, the state of actual rotating machinery is carried out Trend prediction.

In described step (3), calculate all vibration signal x_wN in (), the step of 1.5 dimension spectrums of every group of vibration signal is as follows： I) N number of data in every group of data of all vibration signals is all divided into K section, every section of M data, every segment data is remembered as one Record；II) average is carried out to each record, then calculate three-order cumulant, obtain three-order cumulant Mean valueIII) to three-order cumulant mean valueDo one-dimensional Fourier transform, vibrated Spectrums are tieed up in the 1.5 of signal：

In formula, ω_rRepresent frequency, r=1,2 ..., N, N are positive integer；τ is time delay.

Described step II) in, carry out average to each record, then calculate three-order cumulant obtaining three ranks The step of cumulant diagonal slices mean value is as follows：A () is assumedIt is i-th record, wherein, i=1 ..., K, h=0, 1,...,M-1；Its three-order cumulant is asked to i-th recordFor：

In formula, M₁=max (0 ,-τ)；M₂=min (M-1, M-1- τ), τ are time delay；3x is Third-order cumulants；B () is to all Three-order cumulantAverageFor：

In described step (7), using Markov chain, the state of actual rotating machinery is carried out with the step of trend prediction Suddenly as follows：I) utilization state sequence calculates the state transition probability matrix P of Markov chain；II) select any one time point As beginning, with the state in this moment as original state, it is set to P₀=[0 ..., 1 ..., 0], P₀It is the unit row of 1 × 5 Vector, if its p-th component is 1, remaining component is 0 then it represents that system initial state is in p-th state, calculates subsequent time State probability P₁：

P₁=P₀P=[P₁(1),P₁(2),...,P₁(p)], p ∈ E

In formula, P₁P () represents the probability of p-th state appearance；Judge that q-th state of subsequent time predicted occurs general Whether rate meets P₁(q)=max { P₁(p), p ∈ E }, q ∈ E；If meeting, q-th state is that most probable occurs in this moment State, return to step (5) simultaneously judges the possible running status of plant equipment according to the value of q-th state.

Described step I) in, the computational methods of the state transition probability matrix P of described Markov chain are as follows：A () is known The status switch of rotating machinery is { S₁,S₂,…,S_n, state space is E={ 1,2 ..., 5 }, uses n_pqRepresent data sample The frequency of arrival state q, then frequency n is shifted from state p through a step in this_pqMatrix (the n of composition_pq)_p,q∈EFor shifting frequency square Battle array U：

B () will shift the pth row q column element n of frequency matrix U_pqDivided by the summation of each row, the value obtaining is general as transfer Rate f_pq：

According to transition probability f_pqObtain transition probability matrix P=(f_pq) be：

Wherein, p, q ∈ E.

Due to taking above technical scheme, it has advantages below to the present invention：1st, the present invention is due to tiring out using based on high-order 1.5 dimension spectral methods of accumulated amount are analyzed to rotating machinery fault vibration signal, can reduce the variable working condition information such as load Interference to fault characteristic information, is realized fault characteristic information and is separated with non-faulting information, and then improves rotating machinery The accuracy of failure trend prediction.2nd, the present invention utilizes the rotating machinery vibration to collection for the 1.5 dimension spectrum frequency band energy averages Signal is processed, and obtains equipment state sequence, and the state of utilization state sequence pair equipment fault carries out trend prediction, because This, further increase the accuracy of equipment fault trend prediction.The present invention can be extensively in rotating machinery fault trend prediction Middle application.

Brief description

Fig. 1 is the overall flow schematic diagram of the present invention.

Specific embodiment

With reference to the accompanying drawings and examples the present invention is described in detail.

As shown in figure 1, the present invention provides a kind of markov fault trend based on " 1.5 dimension spectrum frequency band energy average " pre- Survey method, it comprises the following steps：

(1) utilize rotor testbed to simulate rotating machinery normal operating condition, adopted using available data collecting device Collection rotor testbed vibration signal x under normal operating conditions_w(n)={ x₁,...,x_N, wherein, N represents every group of data Number, w represents data group, w=1, represents normal operating condition；

(2) rotor testbed is utilized to simulate three kinds of fault degrees of rotating machinery fault, three kinds of fault degrees are designated as Minor failure degree, moderate fault degree and severe fault degree, and gather rotor testbed using available data collecting device Vibration signal x under three kinds of faults_w(n)={ x₁,...,x_N, wherein, N represents every group of data amount check；W represents data group, W=2,3,4, w=2 represent minor failure level state, w=3 represents moderate fault degree state, and w=4 represents severe fault journey Degree state.

(3) all vibration signal x are calculated_w1.5 dimension spectrums of every group of vibration signal, w=1,2,3,4, its concrete steps in (n) As follows：

I) N number of data in every group of data of all vibration signals is all divided into K section, every section of M data, every segment data conduct One record.

II) average is carried out to each record, then calculate three-order cumulant, finally give Third-order cumulants Diagonal slices mean value, its step is as follows：

A () is assumedIt is the individual record of i-th (i=1 ..., K), wherein, h=0,1 ..., M-1；I-th record is asked Its three-order cumulantFor：

In formula, M₁=max (0 ,-τ)；M₂=min (M-1, M-1- τ), τ are time delay；3x is Third-order cumulants.

B () is to all three-order cumulantAverage, obtain mean valueFor：

III) to three-order cumulant mean valueDo one-dimensional Fourier transform, obtain vibration signal 1.5 tie up spectrums is：

In formula, ω_rRepresent frequency, r=1,2 ..., N, N are positive integer.

(4) 1.5 dimension spectrum frequency band energy averages of each group vibration signal are calculated.1.5 dimension spectrum frequency band energy averages are defined as：Will All amplitudes in 1.5 dimension spectral frequency intervals are added up, and then ask for its averageFor：

(5) obtain frequency band energy interval.According to 1.5 dimension spectrum frequency band energy averagesTo rotating machinery fault three Plant fault degree to be quantified, obtain the frequency band energy interval dividing malfunction：Frequency band energy average numerical value is in intervalState classification be normal operating condition, be designated as state 1；Frequency band energy average numerical value is in interval's State classification is minor failure state, is designated as malfunction 2；Frequency band energy average numerical value is in intervalState divide Class is moderate malfunction, is designated as malfunction 3；Frequency band energy average numerical value is in intervalState classification attach most importance to Degree malfunction, is designated as malfunction 4；Frequency band energy average numerical value is in intervalState classification be collapse state, It is designated as malfunction 5.Remember that status switch is：{S₁,S₂,...,S_n, n is state number, is positive integer；State space E=1, 2,...,5}.

(6) gather the vibration signal of actual rotating machinery, this vibration signal is carried out with step (3) to step (4) Operation, obtains 1.5 dimension spectrum frequency band energy averages of each group vibration signal, and the frequency band energy being given in conjunction with step (5) is interval, obtains The status switch of actual rotating machinery：{S₁,S₂,...,S_n}.

(7) using Markov chain, trend prediction is carried out to the state of actual rotating machinery, comprise the following steps that：

I) utilization state sequence calculates the state transition probability matrix P of Markov chain.

A the status switch of rotating machinery known to () is { S₁,S₂,...,S_n, state space be E=1,2 ..., 5 }, use n_pqRepresent in data sample and shift the frequency of arrival state q, then frequency n from state p through a step_pqThe matrix of composition (n_pq)_{P, q ∈ E}For shifting frequency matrix U：

B () will shift the pth row q column element n of frequency matrix U_pqDivided by the summation of each row, the value obtaining is general as transfer Rate f_pq：

According to transition probability f_pqObtain transition probability matrix P=(f_pq) be：

Wherein, p, q ∈ E.

II) select any one time point as beginning, with the state in this moment as original state, be set to P₀= [0 ..., 1 ..., 0], P₀The unit row vector of 1 × 5, if its p-th component be 1, remaining component be 0 then it represents that System initial state is in p-th state, calculates the state probability P of subsequent time₁：

P₁=P₀P=[P₁(1),P₁(2),...,P₁(p)], p ∈ E

In formula, P₁P () represents the probability of p-th state appearance.

Judge whether the probability that q-th state of subsequent time predicted occurs meets P₁(q)=max { P₁(p), p ∈ E }, q ∈E.If meeting, q-th state in the state that this moment is that most probable occurs, return to step (5) according to q-th state Value judges the possible running status of plant equipment.If q=1, the plant equipment NextState predicting is normal operation shape State；If q=2, the plant equipment NextState predicting is minor failure state；If q=3, the plant equipment that predicts NextState is moderate malfunction；If q=4, the plant equipment NextState predicting is severe malfunction；If q= 5, then the plant equipment NextState predicting is collapse state.

The various embodiments described above are merely to illustrate the present invention, and the structure of wherein each part, connected mode etc. are all can be Change, every equivalents carrying out on the basis of technical solution of the present invention and improvement, all should not exclude the present invention's Outside protection domain.

Claims (5)

1. a kind of markov failure trend prediction method, the method be based on 1.5 dimension spectrum frequency band energy averages realize, it include with Lower step：

(1) utilize rotor testbed to simulate rotating machinery normal operating condition, turned using the collection of available data collecting device Sub- experimental bench vibration signal x under normal operating conditions_w(n)={ x₁,...,x_N, wherein, N represents every group of data amount check, w Represent data group, w=1, represent normal operating condition；

(2) rotor testbed is utilized to simulate minor failure degree, moderate fault degree and the severe event of rotating machinery fault Three kinds of fault degrees of barrier degree, and gather vibration signal under three kinds of faults for the rotor testbed using available data collecting device x_w(n)={ x₁,...,x_N, wherein, N represents every group of data amount check；W=2,3,4 represent data group, and w=2 represents slightly event Barrier level state, w=3 represents moderate fault degree state, and w=4 represents severe fault degree state；

(3) all vibration signal x are calculated_w1.5 dimension spectrums of every group of vibration signal in (n)；

(4) 1.5 dimension spectrum frequency band energy averages of each group vibration signal are calculated

${\stackrel{\‾}{S}}_{w,3x}=\frac{1}{N}\underset{r=1}{\overset{N}{\mathrm{\Σ}}}{S}_{w,3x}\left({\mathrm{\ω}}_r\right),$

In formula, S_w,3x(ω_r) tie up spectrum for the 1.5 of vibration signal；ω_rRepresent frequency, r=1,2 ..., N, N are positive integer；

(5) obtain frequency band energy interval：According to 1.5 dimension spectrum frequency band energy averagesThree kinds of events to rotating machinery fault Barrier degree is quantified, and obtains the frequency band energy interval dividing malfunction：Frequency band energy average numerical value is in interval's State classification is normal operating condition, is designated as state 1；Frequency band energy average numerical value is in intervalState classification be Minor failure state, is designated as malfunction 2；Frequency band energy average numerical value is in intervalState classification be moderate therefore Barrier state, is designated as malfunction 3；Frequency band energy average numerical value is in intervalState classification be severe fault shape State, is designated as malfunction 4；Frequency band energy average numerical value is in intervalState classification be collapse state, be designated as fault State 5；Remember that status switch is：{S₁,S₂,...,S_n, n is state number, is positive integer；State space E=1,2 ..., 5 }；

(6) gather the vibration signal of actual rotating machinery, this vibration signal carried out with step (3) to the operation of step (4), Obtain 1.5 dimension spectrum frequency band energy averages of each group vibration signal, the frequency band energy providing in conjunction with step (5) is interval, obtains actual The status switch of rotating machinery：{S₁,S₂,...,S_n}；

(7) using Markov chain, trend prediction is carried out to the state of actual rotating machinery.

2. as claimed in claim 1 a kind of markov failure trend prediction method it is characterised in that：In described step (3), Calculate all vibration signal x_wN in (), the step of 1.5 dimension spectrums of every group of vibration signal is as follows：

I) N number of data in every group of data of all vibration signals is all divided into K section, every section of M data, every segment data is as one Record；

II) average is carried out to each record, then calculate three-order cumulant, obtain three-order cumulant Mean value

III) to three-order cumulant mean valueDo one-dimensional Fourier transform, obtain 1.5 dimensions of vibration signal Compose and be：

$S_{w,3x}\left({\mathrm{\ω}}_r\right)=\underset{\mathrm{\τ}=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}{\hat{c}}_{w,3x}(\mathrm{\τ},\mathrm{\τ})e^{-j\mathrm{\ω}\mathrm{\τ}},$

In formula, ω_rRepresent frequency, r=1,2 ..., N, N are positive integer；τ is time delay.

3. as claimed in claim 2 a kind of markov failure trend prediction method it is characterised in that：Described step II) in, Carry out average to each record, then calculate three-order cumulant obtaining three-order cumulant mean value Step is as follows：

A () is assumedIt is i-th record, wherein, i=1 ..., K, h=0,1 ..., M-1；Its three rank is asked to i-th record Cumulant diagonal slicesFor：

$x_{w,3x}^i(\mathrm{\τ},\mathrm{\τ})=\frac{1}{M}\underset{h=M_1}{\overset{h=M_2}{\mathrm{\Σ}}}{x}_w^i\left(h\right)x_w^i(h+\mathrm{\τ})x_w^i(h+\mathrm{\τ}),$

In formula, M₁=max (0 ,-τ)；M₂=min (M-1, M-1- τ), τ are time delay；3x is Third-order cumulants；

B () is to all three-order cumulantAverageFor：

${\hat{c}}_{w,3x}(\mathrm{\τ},\mathrm{\τ})=\frac{1}{K}\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{x}_{w,3x}^i(\mathrm{\τ},\mathrm{\τ}).$

4. a kind of markov failure trend prediction method as described in claim 1 or 2 or 3 it is characterised in that：Described step (7), in, the step carrying out trend prediction to the state of actual rotating machinery using Markov chain is as follows：

I) utilization state sequence calculates the state transition probability matrix P of Markov chain；

II) select any one time point as beginning, with the state in this moment as original state, be set to P₀=[0 ..., 1 ..., 0], P₀It is the unit row vector of 1 × 5, if its p-th component is 1, remaining component is 0 then it represents that system is initial State is in p-th state, calculates the state probability P of subsequent time₁：

P₁=P₀P=[P₁(1),P₁(2),…,P₁(p)], p ∈ E

In formula, P₁P () represents the probability of p-th state appearance；Judge that the probability that q-th state of subsequent time of prediction occurs is No meet P₁(q)=max { P₁(p), p ∈ E }, q ∈ E；If meeting, q-th state is the shape that most probable occurs in this moment State, return to step (5) simultaneously judges the possible running status of plant equipment according to the value of q-th state.

5. as claimed in claim 4 a kind of markov failure trend prediction method it is characterised in that：Described step I) in, The computational methods of the state transition probability matrix P of described Markov chain are as follows：

A the status switch of rotating machinery known to () is { S₁,S₂,…,S_n, state space is E={ 1,2 ..., 5 }, uses n_pq Represent in data sample and shift the frequency of arrival state q, then frequency n from state p through a step_pqMatrix (the n of composition_pq)_p,q∈EFor Transfer frequency matrix U：

B () will shift the pth row q column element n of frequency matrix U_pqDivided by the summation of each row, the value obtaining is as transition probability f_pq：

$f_{pq}=\frac{n_{pq}}{{\mathrm{\Σ}}_{q=1}^K{n}_{pq}},\∀p,q\∈\{1,2,\mathrm{...},5\};$

According to transition probability f_pqObtain transition probability matrix P=(f_pq) be：

Wherein, p, q ∈ E.