CN104156591A - 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, particularly the markov failure trend prediction method based on " 1.5 dimension spectrum frequency band energy average " about one.

Background technology

Safety, the stable operation of rotating machinery have material impact to economy and society, adopt safety, the stable operation of scientific and effective method support equipment to have positive meaning.Rotating machinery has a development and change process by normal operating condition is deteriorated for malfunction, if can adopt rational Forecasting Methodology, its malfunction is carried out to effective trend prediction, be conducive to implement advanced anticipatory maintenance and initiatively maintenance, avoid the generation of accident, reduce economic loss.

Summary of the invention

For the problems referred to above, the object of this invention is to provide a kind of markov failure trend prediction method, the method can effectively be predicted the development and change situation of rotating machinery fault, improves the accuracy of failure trend prediction.

For achieving the above object, the present invention takes following technical scheme: a kind of markov failure trend prediction method, the method realizes based on 1.5 dimension spectrum frequency band energy averages, it comprises the following steps: (1) utilizes rotor experiment table simulation rotating machinery normal operating condition, utilizes available data collecting device to gather the vibration signal x of rotor experiment table under normal operating condition _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check, w representative data group, and w=1, represents normal operating condition; (2) utilize minor failure degree, moderate fault degree and three kinds of fault degrees of severe fault degree of rotor experiment table simulation rotating machinery fault, and utilize available data collecting device to gather the vibration signal x of rotor experiment table under three kinds of faults _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check; W=2,3,4 representative data groups, w=2 represents minor failure degree state, and w=3 represents moderate fault degree state, and w=4 represents severe fault degree state; (3) calculate all vibration signal x _w(n) 1.5 of every group of vibration signal dimension spectrums in; (4) 1.5 dimensions of calculating each group of vibration signal are composed frequency band energy averages

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

In formula, S _{w, 3x}(ω _r) be 1.5 dimension spectrums of vibration signal; ω _rrepresent frequency, r=1,2 ... N, N is positive integer; (5) obtain frequency band energy interval: according to 1.5 dimension spectrum frequency band energy averages three of rotating machinery fault kinds of fault degrees are quantized, obtain the frequency band energy interval of dividing malfunction: frequency band energy average numerical value is in interval state classification be normal operating condition, be designated as state 1; Frequency band energy average numerical value is in interval state classification be minor failure state, be designated as malfunction 2; Frequency band energy average numerical value is in interval state classification be moderate malfunction, be designated as malfunction 3; Frequency band energy average numerical value is in interval state classification be severe malfunction, be designated as malfunction 4; Frequency band energy average numerical value is in interval state classification be collapse state, be designated as malfunction 5; Note status switch is: { S ₁, S ₂... 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 to the operation of step (3) to step (4), obtain 1.5 dimension spectrum frequency band energy averages of each group of vibration signal, the frequency band energy interval that integrating step (5) provides, obtains the status switch of actual rotating machinery: { S ₁, S ₂... S _n; (7) utilize Markov chain to carry out trend prediction to the state of actual rotating machinery.

In described step (3), calculate all vibration signal x _w(n) in, the step of 1.5 of every group of vibration signal dimension spectrums is as follows: I) N data in every group of data of all vibration signals are all divided into K section, every section of M data, every segment data is as a record; II) each record is gone to average, then calculate three semi-invariant diagonal angle, rank sections, obtain three semi-invariant diagonal angle, rank section mean values iII) to three semi-invariant diagonal angle, rank section mean values do one-dimensional Fourier transform, the 1.5 dimension spectrums that obtain vibration signal are:

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

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

Described step II) in, each record is gone to average, then it is as follows to calculate the step that three semi-invariant diagonal angles, rank sections obtain three semi-invariant diagonal angles, rank section mean values: (a) hypothesis i record, wherein, i=1 ... K, h=0,1 ... M-1; I record asked to its semi-invariant diagonal angle, three rank section for:

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

In formula, M ₁=max (0 ,-τ); M ₂=min (M-1, M-1-τ), τ is time delay; 3x is three rank semi-invariants; (b) to all three semi-invariant diagonal angle, rank sections average for:

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

In described step (7), the step of utilizing Markov chain to carry out trend prediction to the state of actual rotating machinery is as follows: I) utilize status switch to calculate the state transition probability matrix P of Markov chain; II) select any one time point as beginning, taking the state in this moment as original state, be made as P ₀=[0 ..., 1 ... 0], P ₀be the unit row vector of 1 × 5, if its p component is 1, all the other components are 0, represent that system initial state is in p state, calculate the state probability P in next moment ₁:

P ₁＝P ₀P＝[P ₁(1),P ₁(2),...P ₁(p)]，p∈E

In formula, P ₁(p) represent the probability that p state occurs; Whether the probability that judges next moment q state appearance of prediction meets P ₁(q)=max{P ₁(p), p ∈ E}, q ∈ E; If meet, q state is the state that most probable occurs in this moment, returns to step (5) and judges according to the value of q state the running status that plant equipment is possible.

Described step I) in, the computing method of the state transition probability matrix P of described Markov chain are as follows: (a) status switch of known rotating machinery is { S ₁, S ₂... S _n, state space is E={1,2 ..., 5}, uses n _pqrepresent to shift through a step from state p in data sample the frequency of arrival state q, frequency n _pqmatrix (the n of composition _pq) _{p, q ∈ E}for shifting frequency matrix U:

(b) the capable q column element of the p n of frequency matrix U will be shifted _pqdivided by the summation of each row, the value obtaining is as transition probability f _pq:

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

According to transition probability f _pqobtain transition probability matrix P=(f _pq) be:

Wherein, p, q ∈ E.

The present invention is owing to taking above technical scheme, it has the following advantages: 1, the present invention is owing to adopting the 1.5 dimension spectral methods based on Higher Order Cumulants to analyze rotating machinery fault vibration signal, can reduce the interference of the variable working condition information such as load to fault characteristic information, realize separating of fault characteristic information and non-failure message, and then improve the accuracy of rotating machinery failure trend prediction.2, the present invention utilizes 1.5 dimension spectrum frequency band energy averages to process the rotating machinery vibration signal gathering, equipment status switch, and utilize status switch to carry out trend prediction to the state of equipment failure, therefore, further improve the accuracy of equipment failure trend prediction.The present invention can extensively apply in rotating machinery fault trend prediction.

Brief description of the drawings

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

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail.

As shown in Figure 1, the invention provides a kind of markov failure trend prediction method based on " 1.5 dimension spectrum frequency band energy average ", it comprises the following steps:

(1) utilize rotor experiment table simulation rotating machinery normal operating condition, utilize available data collecting device to gather the vibration signal x of rotor experiment table under normal operating condition _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check, w representative data group, and w=1, represents normal operating condition;

(2) utilize rotor experiment table 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 utilize available data collecting device to gather the vibration signal x of rotor experiment table under three kinds of faults _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check; W representative data group, w=2,3,4, w=2 represents minor failure degree state, and w=3 represents moderate fault degree state, and w=4 represents severe fault degree state.

(3) calculate all vibration signal x _w(n) 1.5 of every group of vibration signal dimension spectrums in, w=1,2,3,4, its concrete steps are as follows:

I) N data in every group of data of all vibration signals are all divided into K section, every section of M data, every segment data is as a record.

II) each record is gone to average, then calculate three semi-invariant diagonal angle, rank sections, and finally obtaining three semi-invariant diagonal angle, rank section mean values, its step is as follows:

(a) suppose be i (i=1 ... K) individual record, wherein, h=0,1 ... M-1; I record asked to its semi-invariant diagonal angle, three rank section for:

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

In formula, M ₁=max (0 ,-τ); M ₂=min (M-1, M-1-τ), τ is time delay; 3x is three rank semi-invariants.

(b) to all three semi-invariant diagonal angle, rank sections average, obtain mean value for:

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

III) to three semi-invariant diagonal angle, rank section mean values do one-dimensional Fourier transform, the 1.5 dimension spectrums that obtain vibration signal are:

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

In formula, ω _rrepresent frequency, r=1,2 ... N, N is positive integer.

(4) 1.5 dimensions of calculating each group of vibration signal are composed frequency band energy averages.1.5 dimension spectrum frequency band energy averages are defined as: all amplitudes in 1.5 dimension spectral frequency intervals are added up, then ask for its average for:

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

(5) obtain frequency band energy interval.According to 1.5 dimension spectrum frequency band energy averages three of rotating machinery fault kinds of fault degrees are quantized, obtain the frequency band energy interval of dividing malfunction: frequency band energy average numerical value is in interval state classification be normal operating condition, be designated as state 1; Frequency band energy average numerical value is in interval state classification be minor failure state, be designated as malfunction 2; Frequency band energy average numerical value is in interval state classification be moderate malfunction, be designated as malfunction 3; Frequency band energy average numerical value is in interval state classification be severe malfunction, be designated as malfunction 4; Frequency band energy average numerical value is in interval state classification be collapse state, be designated as malfunction 5.Note status switch is: { S ₁, S ₂... 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 to the operation of step (3) to step (4), obtain 1.5 dimension spectrum frequency band energy averages of each group of vibration signal, the frequency band energy interval that integrating step (5) provides, obtains the status switch of actual rotating machinery: { S ₁, S ₂... S _n.

(7) utilize Markov chain to carry out trend prediction to the state of actual rotating machinery, concrete steps are as follows:

I) utilize status switch to calculate the state transition probability matrix P of Markov chain.

(a) status switch of known rotating machinery is { S ₁, S ₂... S _n, state space is E={1,2 ..., 5}, uses n _pqrepresent to shift through a step from state p in data sample the frequency of arrival state q, frequency n _pqmatrix (the n of composition _pq) _{p, q ∈ E}for shifting frequency matrix U:

(b) the capable q column element of the p n of frequency matrix U will be shifted _pqdivided by the summation of each row, the value obtaining is as transition probability f _pq:

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

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, taking the state in this moment as original state, be made as P ₀=[0 ..., 1. .., P ₀be the unit row vector of 1 × 5, if its p component is 1, all the other components are 0, represent that system initial state is in p state, calculate the state probability P in next moment ₁:

P ₁＝P ₀P＝[P ₁(1),P ₁(2),...P ₁(p)]，p∈E

In formula, P ₁(p) represent the probability that p state occurs.

Whether the probability that judges next moment q state appearance of prediction meets P ₁(q)=max{P ₁(p), p ∈ E}, q ∈ E.If meet, q state is the state that most probable occurs in this moment, returns to step (5) and judges according to the value of q state the running status that plant equipment is possible.If q=1, the plant equipment NextState doping is normal operating condition; If q=2, the plant equipment NextState doping is minor failure state; If q=3, the plant equipment NextState doping is moderate malfunction; If q=4, the plant equipment NextState doping is severe malfunction; If q=5, the plant equipment NextState doping is collapse state.

The various embodiments described above are only for illustrating the present invention, and wherein structure, the connected mode etc. of each parts all can change to some extent, and every equivalents of carrying out on the basis of technical solution of the present invention and improvement, all should not get rid of outside protection scope of the present invention.

Claims (5)

1. a markov failure trend prediction method, the method realizes based on 1.5 dimension spectrum frequency band energy averages, and it comprises the following steps:

(1) utilize rotor experiment table simulation rotating machinery normal operating condition, utilize available data collecting device to gather the vibration signal x of rotor experiment table under normal operating condition _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check, w representative data group, and w=1, represents normal operating condition;

(2) utilize minor failure degree, moderate fault degree and three kinds of fault degrees of severe fault degree of rotor experiment table simulation rotating machinery fault, and utilize available data collecting device to gather the vibration signal x of rotor experiment table under three kinds of faults _w(n)={ x ₁... x _n, wherein, N represents every group of data amount check; W=2,3,4 representative data groups, w=2 represents minor failure degree state, and w=3 represents moderate fault degree state, and w=4 represents severe fault degree state;

(3) calculate all vibration signal x _w(n) 1.5 of every group of vibration signal dimension spectrums in;

(4) 1.5 dimensions of calculating each group of vibration signal are composed frequency band energy averages

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

In formula, S _{w, 3x}(ω _r) be 1.5 dimension spectrums of vibration signal; ω _rrepresent frequency, r=1,2 ... N, N is positive integer;

(5) obtain frequency band energy interval: according to 1.5 dimension spectrum frequency band energy averages three of rotating machinery fault kinds of fault degrees are quantized, obtain the frequency band energy interval of dividing malfunction: frequency band energy average numerical value is in interval state classification be normal operating condition, be designated as state 1; Frequency band energy average numerical value is in interval state classification be minor failure state, be designated as malfunction 2; Frequency band energy average numerical value is in interval state classification be moderate malfunction, be designated as malfunction 3; Frequency band energy average numerical value is in interval state classification be severe malfunction, be designated as malfunction 4; Frequency band energy average numerical value is in interval state classification be collapse state, be designated as malfunction 5; Note status switch is: { S ₁, S ₂... 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 to the operation of step (3) to step (4), obtain 1.5 dimension spectrum frequency band energy averages of each group of vibration signal, the frequency band energy interval that integrating step (5) provides, obtains the status switch of actual rotating machinery: { S ₁, S ₂... S _n;

(7) utilize Markov chain to carry out trend prediction to the state of actual rotating machinery.

2. a kind of markov failure trend prediction method as claimed in claim 1, is characterized in that: in described step (3), calculate all vibration signal x _w(n) in, the step of 1.5 of every group of vibration signal dimension spectrums is as follows:

I) N data in every group of data of all vibration signals are all divided into K section, every section of M data, every segment data is as a record;

II) each record is gone to average, then calculate three semi-invariant diagonal angle, rank sections, obtain three semi-invariant diagonal angle, rank section mean values

III) to three semi-invariant diagonal angle, rank section mean values do one-dimensional Fourier transform, the 1.5 dimension spectrums that obtain vibration signal are:

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

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

3. a kind of markov failure trend prediction method as claimed in claim 2, it is characterized in that: described step II) in, each record is gone to average, then it is as follows to calculate the step that three semi-invariant diagonal angles, rank sections obtain three semi-invariant diagonal angles, rank section mean values:

(a) suppose i record, wherein, i=1 ... K, h=0,1 ... M-1; I record asked to its semi-invariant diagonal angle, three rank section for:

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

In formula, M ₁=max (0 ,-τ); M ₂=min (M-1, M-1-τ), τ is time delay; 3x is three rank semi-invariants;

(b) to all three semi-invariant diagonal angle, rank sections average for:

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

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

I) utilize status switch to calculate the state transition probability matrix P of Markov chain;

II) select any one time point as beginning, taking the state in this moment as original state, be made as P ₀=[0 ..., 1. .., P ₀be the unit row vector of 1 × 5, if its p component is 1, all the other components are 0, represent that system initial state is in p state, calculate the state probability P in next moment ₁:

P ₁＝P ₀P＝[P ₁(1),P ₁(2),...P ₁(p)]，p∈E

In formula, P ₁(p) represent the probability that p state occurs; Whether the probability that judges next moment q state appearance of prediction meets P ₁(q)=max{P ₁(p), p ∈ E}, q ∈ E; If meet, q state is the state that most probable occurs in this moment, returns to step (5) and judges according to the value of q state the running status that plant equipment is possible.

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

(a) status switch of known rotating machinery is { S ₁, S ₂... S _n, state space is E={1,2 ..., 5}, uses n _pqrepresent to shift through a step from state p in data sample the frequency of arrival state q, frequency n _pqmatrix (the n of composition _pq) _{p, q ∈ E}for shifting frequency matrix U:

(b) the capable q column element of the p n of frequency matrix U will be shifted _pqdivided by the summation of each row, the value obtaining is as transition probability f _pq:

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

According to transition probability f _pqobtain transition probability matrix P=(f _pq) be:

Wherein, p, q ∈ E.