CN106248381B - A kind of rolling bearing life dynamic prediction method based on multiple features and phase space - Google Patents
A kind of rolling bearing life dynamic prediction method based on multiple features and phase space Download PDFInfo
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Abstract
A kind of rolling bearing life dynamic prediction method based on multiple features and phase space first obtains the vibration signal of rolling bearing, extracts its time domain and frequency domain character index, be standardized respectively and sliding handles to obtain relative characteristic index；Then multiple characteristic indexs are merged using PCA technology, obtains a comprehensive decline performance index series and carries out life prediction；The comprehensive decline performance indicator of history degenerative process is subjected to phase space reconfiguration again, is compared in phase space with current degradation process, obtains the out-of-service time of a prediction；The out-of-service time of this prediction and history out-of-service time are finally matched into its probability density distribution of combinational estimation, calculate average life span；And expanded by the continuous accumulation of analysis sample, the average life span at different observation moment is obtained, the present invention can effectively reflect effect multifactor in rolling bearing degenerative process, not by the constraint of assumed condition, prediction error is reduced simultaneously, realizes service life dynamic and is accurately predicted.
Description
Technical field
The present invention relates to rolling bearing life electric powder predictions, and in particular to a kind of rolling based on multiple features and phase space
Dynamic bearing service life dynamic prediction method.
Background technique
Rolling bearing is as one of components important in mechanical equipment and critical component easy to damage, performance and reliable
Property plays a crucial role the performance and reliability service of entire mechanical equipment.Rolling bearing life is predicted
According to its current degenerate state, predict that it fails the time used from bringing into operation to occurring, consequently facilitating in a planned way pacifying
It lists and indexes and repairs, lay the foundation for the maintenance decision of equipment.Therefore, precognition of the service life to equipment of rolling bearing in operational process is predicted
Maintenance is of great significance.
The selection of performance indicator is most important to accurate predicted roll bearing life, and traditional life prediction is with vibration signal
One feature is predicted as decline performance indicator, cannot effectively reflect work multifactor in rolling bearing degenerative process
With.Due to rolling bearing degenerative process have the characteristics that it is non-linear and non-stationary, tradition pass through BP neural network and supporting vector
Machine scheduling algorithm establish Life Prediction Model carry out life prediction method by assumed condition constraint, and prediction early stage by
Observation sample quantity lacks and the influence of random error, keeps prediction result error larger, cannot achieve the accurate of rolling bearing life
With dynamic prediction.
Summary of the invention
In order to overcome the disadvantages of the above prior art, the purpose of the present invention is to provide one kind to be based on multiple features and phase space
Rolling bearing life dynamic prediction method, can effectively reflect effect multifactor in rolling bearing degenerative process, and not by
The constraint of assumed condition in life prediction reduces in prediction early stage by observation sample quantity caused by few and random errors affect
Error is predicted, to realize the service life dynamic of rolling bearing and accurately predict.
To achieve the goals above, the technical scheme adopted by the invention is as follows:
A kind of rolling bearing life dynamic prediction method based on multiple features and phase space, comprising the following steps:
The first step obtains the vibration signal of rolling bearing, extracts its multiple time domain and frequency domain character index；
Time domain and frequency domain character index are standardized respectively and sliding handle to obtain relative characteristic index by second step,
Steps are as follows for calculating:
Step 1: arbitrarily choosing the characteristic value of one section of Trend Stationary in the normal phase, calculate the average of this section of characteristic value；
Step 2: calculating the ratio between primitive character value and average, obtain a relative characteristic index；
Step 3: M point being carried out to relative characteristic index and slides average treatment, M=5~20, xRRXFor primitive character and averagely
Several ratio；xMAFor through sliding it is average after sequence, i.e., final relative characteristic index, calculation formula is as follows:
Third step merges multiple characteristic indexs using PCA technology, obtains a comprehensive decline performance index series
Carry out life prediction；
The comprehensive decline performance indicator of history degenerative process is carried out phase space reconfiguration by the 4th step, in phase space with work as
Preceding degenerative process compares, and obtains the out-of-service time of a prediction；
The out-of-service time of this prediction and history out-of-service time are matched its probability density distribution of combinational estimation by the 5th step,
Calculate average life span；
6th step is constantly accumulated expansion analysis sample by contraction time window, obtains the average life span at different observation moment.
Specific step is as follows for the third step:
Step 1: zero-mean processing, X are carried out to original matrixi=[xi1,xi2,…,xin]TFor i-th of relative characteristic index
Sequence, time domain and frequency domain character index is normalized and the original matrix of sliding treated relative characteristic index composition are as follows:
Step 2: carrying out linear transformation and obtain about X1,X2,…XpLinear combination:
Y1=a11X1+a12X2+…+a1pXp
Y2=a21X1+a22X2+…+a2pXp
Yp=ap1X1+ap2X2+…+appXp；
By linear transformation, a new coordinate system Y is obtained1,Y2,…,Yp, Y1,Y2,…,YpIt is the first of original variable,
Second ..., pth principal component, and it is mutually irrelevant；I-th of principal component of original variable is with the covariance matrix of original matrix X
Ith feature value λiFeature vector (a after corresponding standardizationi1,ai2,…,aip) be coefficient linear combination, by eigenvalue λ by
Minispread is arrived greatly, obtains the first, the second by linear combination ..., p-th of principal component；
Step 3: the life prediction using first principal component as the comprehensive performance indicator that fails, for rolling bearing.
The detailed process of 4th step are as follows:
Step 1: assuming that there is the comprehensive decline performance index series of M group history degenerative process, these index series being carried out
Phase space reconfiguration realizes that the dynamics track of rolling bearing degenerative process is fully deployed in phase space；
Step 2: the study of Degradation path function in phase space, using radial base (RBF) neural network to nonlinear function
Excellent approximation capability obtains nonlinear loci function, and Degradation path function in phase space is realized by RBF neural
It practises；
Assuming that the comprehensive decline performance index series of i-th group of history degenerative process is Xi={ xi(t1),xi(t2),…,xi
(tn), wherein i=1,2 ..., M, n are the length of i-th group of index series, k=1,2 ... L.L=n- (mi-1)τiBy mutually empty
Between reconstruct after vector are as follows:
xxik(t)={ xi(tk),xi(tk+τi),…,xi(tk+(mi-1)τi)}
By the vector { xx after reconstructik(t) | k=1,2 ..., L } and corresponding active time { tk| k=1,2 ..., L } point
Not as the training for carrying out RBF neural is output and input, the trajectory of phase space function of i-th group of history degenerative process is obtained,
Other each group history degenerative processes all undergo identical training to obtain different lopcus functions；
Step 3: the prediction out-of-service time, it is assumed that currently needing the degenerative process predicted is the M+1 times degenerative process, at this
The observation moment carries out predicting that corresponding runing time is TM+1, the comprehensive decline performance index series of foundation is { xM+1(t1),xM+1
(t2),…,xM+1(tn), phase space reconfiguration is carried out to the sequence, reconstructed vector is input to the RBF after the completion of training through network
In learnt, obtain one group of estimation runing time vector [T1,T2,…TM], calculate the runing time and actual run time
Deviation:
ei=(Ti-TM+1)2I=1,2 ... M
Then in moment TM+1Place obtains an error vector e=[e1,e2,…,eM], thus obtain the moment Degradation path with
The similarity degree of history Degradation path:
tM+1For the out-of-service time of current time prediction, tiFor rolling bearing history service life, according to similarity degree and go through
Rolling bearing can be predicted in the out-of-service time at current time in history service life:
When predicting next time, performance indicator data are expanded by telescopic window, step more than repetition obtains one newly accidentally
New error vector is added with the error vector of last computation and is assigned to new error vector again by difference vector.
The detailed process of 5th step are as follows:
Step 1: history out-of-service time and the out-of-service time of current predictive are carried out matching as input by input sample data
Sample, it is assumed that current predictive is in kth observation, and obtained sample set isWherein m is sample point
Number；
Step 2: exptended sample, original input sample XkNew sample Y is obtained after expanding by RBF neuralk={ y1,
y2,…,yn, wherein n is sample points after expanding, and n > m；
Step 3: probability Estimation, σ is smoothing factor, after data normalizationThis is estimated using cuclear density method
Observe the probability density distribution of out-of-service time at moment:
Step 4: replacing the variable y in above formula with variable t, then obtain average life span are as follows:
Advantages of the present invention are as follows:
1. establishing more effective, more comprehensively reaction rolling bearing degradation information a synthesis degenerative by PCA technology
It can index progress life prediction.
2. the comparison of history Degradation path and current degradation track is realized by phase space reconstruction technique, it is not pre- by the service life
The constraint of assumed condition in survey.
3. realizing the estimation of average life span by the probability density distribution of estimation rolling bearing out-of-service time, reducing
The prediction error generated less by early stage observation sample, and as the accumulation dynamic of observation sample updates prediction result, it improves pre-
The accuracy of survey.
Detailed description of the invention
Fig. 1 is the flow chart of the embodiment of the present invention.
Fig. 2 is that the comprehensive decline performance indicator of 6 groups of embodiment trained rolling bearings changes over time curve graph.
Fig. 3 is that the comprehensive decline performance indicator of tested rolling bearing changes over time curve graph.
Fig. 4 is the comparison diagram of current degradation process Yu history degenerative process.
Fig. 5 is the dynamic probability model figure of out-of-service time.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
Referring to Fig.1, a kind of rolling bearing life dynamic prediction method based on multiple features and phase space, including following step
It is rapid:
The first step obtains the vibration signal of rolling bearing, extracts its time domain and frequency domain character index, such as table 1, table 2 and table 3
It is shown, x={ x1,x2,…,xNIt is vibration signal,
Table 1 has dimension time domain index
2 non_dimensional time domain index of table
In frequency-domain index calculating, s (k) is the frequency spectrum of signal x, and k=1,2 ..., K, K is spectral line number, fkIt is kth item spectrum
The frequency values of line,
3 frequency-domain index of table
Time domain and frequency domain character index are standardized by second step respectively in order to reduce the difference between different bearings
It handles to obtain relative characteristic index with sliding, steps are as follows for calculating:
Step 1: arbitrarily choosing the characteristic value of one section of Trend Stationary in the normal phase, calculate the average of this section of characteristic value；
Step 2: calculating the ratio between primitive character value and average, obtain a relative characteristic index；
Step 3: M point being carried out to relative characteristic index above and slides average treatment, M=5~20, xRRXFor primitive character
With the ratio of average；xMAFor through sliding it is average after sequence, i.e., final relative characteristic index, calculation formula is as follows:
Third step merges multiple characteristic indexs using PCA technology, and rolling bearing can more effectively be reacted by obtaining one
The comprehensive decline performance index series of degenerative process carries out life prediction, the specific steps are as follows:
Step 1: zero-mean processing, X are carried out to original matrixi=[xi1,xi2,…,xin]TFor i-th of relative characteristic index
Sequence, time domain and frequency domain character index is normalized and the original matrix of sliding treated relative characteristic index composition are as follows:
Step 2: carrying out linear transformation and obtain about X1,X2,…XpLinear combination:
Y1=a11X1+a12X2+…+a1pXp
Y2=a21X1+a22X2+…+a2pXp
Yp=ap1X1+ap2X2+…+appXp；
By linear transformation, a new coordinate system Y is obtained1,Y2,…,Yp, Y1,Y2,…,YpIt is the first of original variable,
Second ..., pth principal component, and it is mutually irrelevant；I-th of principal component of original variable is with the covariance matrix of original matrix X
Ith feature value λiFeature vector (a after corresponding standardizationi1,ai2,…,aip) be coefficient linear combination, by eigenvalue λ by
Minispread is arrived greatly, obtains the first, the second by linear combination ..., p-th of principal component；
Step 3: the life prediction using first principal component as the comprehensive performance indicator that fails, for rolling bearing；Referring to Fig. 2
And Fig. 3, Fig. 2 change over time curve graph for the comprehensive decline performance indicator of 6 groups of trained rolling bearings, Fig. 3 is predicted roll axis
The comprehensive decline performance indicator held changes over time curve graph；
The comprehensive decline performance indicator of history degenerative process is carried out phase space reconfiguration by the 4th step, in phase space with work as
Preceding degenerative process compares, and obtains the out-of-service time of a prediction, and process is as shown in Figure 4；
The phase space reconfiguration of this patent uses coordinate delay reconstruction method, it is assumed that Nonlinear Time Series are X={ x (t1),x
(t2),…,x(tn), if m and τ are Embedded dimensions and the delay time of the sequence, therefore, L insertion can be generated in phase space
Point, L=n- (m-1) τ, wherein (m-1) τ is the time delay window of the sequence；
According to time delay thought, phase space vector such as following formula after time series reconstruct, wherein xxkIt (t) is phase space
In a point:
xxk(t)=[x (tk),x(tk+τ),…,x(tk+ (m-1) τ)], k=1,2 ..., L
Rolling bearing history degenerative process has important reference value to the prediction for being currently undergoing similar process, therefore
Establish history degradation model by the comprehensive decline performance index series of history degenerative process, on the basis of history degradation model with
Current degradation process compares, and detailed process is as follows:
Step 1: assuming that there is the comprehensive decline performance index series of M group history degenerative process, these index series being carried out
Phase space reconfiguration realizes that the dynamics track of rolling bearing degenerative process is fully deployed in phase space；
Step 2: the study of Degradation path function in phase space, the analytical expression of history Degradation path function in phase space
It cannot directly give, but obtain non-linear rail using radial base (RBF) the neural network approximation capability excellent to nonlinear function
Trace function realizes the study of Degradation path function in phase space by RBF neural；
The quantity of neural network is determined by the quantity of history degenerative process, it is assumed that the synthesis of i-th group of history degenerative process
Decline performance index series is Xi={ xi(t1),xi(t2),…,xi(tn), wherein i=1,2 ..., M, n are i-th group of index sequence
The length of column, k=1,2 ... L.L=n- (mi-1)τiThe vector after phase space reconfiguration are as follows:
xxik(t)={ xi(tk),xi(tk+τi),…,xi(tk+(mi-1)τi)}
By the vector { xx after reconstructik(t) | k=1,2 ..., L } and corresponding active time { tk| k=1,2 ..., L } point
Not as the training for carrying out RBF neural is output and input, the trajectory of phase space function of i-th group of history degenerative process is obtained,
Other each group history degenerative processes all undergo identical training to obtain different lopcus functions；
Step 3: the prediction out-of-service time, it is assumed that currently needing the degenerative process predicted is the M+1 times degenerative process, at this
The observation moment carries out predicting that corresponding runing time is TM+1, the comprehensive decline performance index series of foundation is { xM+1(t1),xM+1
(t2),…,xM+1(tn), phase space reconfiguration is carried out to the sequence, reconstructed vector is input to the RBF after the completion of training through network
In learnt, obtain one group of estimation runing time vector [T1,T2,…TM], calculate the runing time and actual run time
Deviation:
ei=(Ti-TM+1)2I=1,2 ... M
Then in moment TM+1Place obtains an error vector e=[e1,e2,…,eM], thus obtain the moment Degradation path with
The similarity degree of history Degradation path:
tM+1For the out-of-service time of current time prediction, tiFor rolling bearing history service life, according to similarity degree and go through
Rolling bearing can be predicted in the out-of-service time at current time in history service life:
When predicting next time, performance indicator data are expanded by telescopic window, step more than repetition obtains one newly accidentally
Difference vector, in order to reduce influence of the exceptional data point to prediction result, by the error vector phase of new error vector and last computation
Exacerbation is newly assigned to new error vector；
The out-of-service time of this prediction and history out-of-service time are matched its probability density distribution of combinational estimation by the 5th step,
Average life span is calculated, as shown in Figure 5；
Early stage is predicted in rolling bearing life, since few by observation data and system noise is influenced, the failure of prediction
Time and actual value deviation are larger, therefore, will be current in order to improve the accuracy of prediction, eliminate the influence of various enchancement factors
The out-of-service time and history degradation failure time of prediction as statistical sample, estimate its probability density distribution, calculate average life span
As the prediction result at current time, detailed process is as follows:
Step 1: history out-of-service time and the out-of-service time of current predictive are carried out matching as input by input sample data
Sample, it is assumed that current predictive is in kth observation, and obtained sample set isWherein m is sample point
Number；
Step 2: exptended sample, original input sample XkNew sample Y is obtained after expanding by RBF neuralk={ y1,
y2,…,yn, wherein n is sample points after expanding, and n > m；
Step 3: probability Estimation, σ is smoothing factor, after data normalizationThis is estimated using cuclear density method
Observe the probability density distribution of out-of-service time at moment:
Step 4: replacing the variable y in above formula with variable t, then obtain average life span are as follows:
6th step is constantly accumulated expansion analysis sample by contraction time window, obtains the average life span at different observation moment,
As shown in table 4.
The average life span of 4 rolling bearing of table prediction
Claims (2)
1. a kind of rolling bearing life dynamic prediction method based on multiple features and phase space, which is characterized in that including following step
It is rapid:
The first step obtains the vibration signal of rolling bearing, extracts its multiple time domain and frequency domain character index；
Time domain and frequency domain character index are standardized respectively and sliding handle to obtain relative characteristic index by second step, calculate
Steps are as follows:
Step 1: arbitrarily choosing the characteristic value of one section of Trend Stationary in the normal phase, calculate the average of this section of characteristic value；
Step 2: calculating the ratio between primitive character value and average, obtain a relative characteristic index；
Step 3: M point being carried out to relative characteristic index and slides average treatment, M=5~20, xRRXFor primitive character and average
Ratio；xMAFor through sliding it is average after sequence, i.e., final relative characteristic index, calculation formula is as follows:
Third step merges multiple characteristic indexs using PCA technology, obtains a comprehensive decline performance index series and carries out
Life prediction；
The comprehensive decline performance indicator of history degenerative process is carried out phase space reconfiguration by the 4th step, in phase space with currently move back
Change process compares, and obtains the out-of-service time of a prediction；
The out-of-service time of this prediction and history out-of-service time are matched its probability density distribution of combinational estimation, calculated by the 5th step
Average life span；
6th step is constantly accumulated expansion analysis sample by contraction time window, obtains the average life span at different observation moment；
The detailed process of 4th step are as follows:
Step 1: assuming that there is the comprehensive decline performance index series of M group history degenerative process, these index series being carried out mutually empty
Between reconstruct, realize rolling bearing degenerative process dynamics track be fully deployed in phase space；
Step 2: the study of Degradation path function in phase space, it is excellent to nonlinear function using radial base (RBF) neural network
Approximation capability obtain nonlinear loci function, pass through RBF neural realize phase space in Degradation path function study；
Assuming that the comprehensive decline performance index series of i-th group of history degenerative process is Xi={ xi(t1),xi(t2),…,xi(tn),
Wherein i=1,2 ..., M, n are the length of i-th group of index series, k=1,2 ... L.L=n- (mi-1)τiBy phase space reconfiguration
Vector afterwards are as follows:
xxik(t)={ xi(tk),xi(tk+τi),…,xi(tk+(mi-1)τi)}
M and τ is Embedded dimensions and the delay time of the sequence,
By the vector { xx after reconstructik(t) | k=1,2 ..., L } and corresponding active time { tk| k=1,2 ..., L } make respectively
For the training for outputting and inputting progress RBF neural, the trajectory of phase space function of i-th group of history degenerative process is obtained, other
Each group history degenerative process all undergoes identical training to obtain different lopcus functions；
Step 3: the prediction out-of-service time, it is assumed that currently needing the degenerative process predicted is the M+1 times degenerative process, in this observation
Moment carries out predicting that corresponding runing time is TM+1, the comprehensive decline performance index series of foundation is { xM+1(t1),xM+1
(t2),…,xM+1(tn), phase space reconfiguration is carried out to the sequence, reconstructed vector is input to the RBF after the completion of training through network
In learnt, obtain one group of estimation runing time vector [T1,T2,…TM], calculate the runing time and actual run time
Deviation:
ei=(Ti-TM+1)2I=1,2 ... M
Then in moment TM+1Place obtains an error vector e=[e1,e2,…,eM], to obtain the moment Degradation path and history
The similarity degree of Degradation path:
tM+1For the out-of-service time of current time prediction, tiFor rolling bearing history service life, taken according to similarity degree and history
Service life predictable rolling bearing is used as a servant in the out-of-service time at current time:
When predicting next time, by telescopic window expand performance indicator data, repeat more than step obtain a new error to
Amount, new error vector is added with the error vector of last computation and is assigned to new error vector again；
The detailed process of 5th step are as follows:
Step 1: history out-of-service time and the out-of-service time of current predictive are carried out matching as input sample by input sample data
This, it is assumed that current predictive is in kth observation, and obtained sample set isWherein m is sample point
Number；
Step 2: exptended sample, original input sample XkNew sample Y is obtained after expanding by RBF neuralk={ y1,
y2,…,yn, wherein n is sample points after expanding, and n > m；
Step 3: probability Estimation, σ is smoothing factor, after data normalizationThis observation is estimated using cuclear density method
The probability density distribution of out-of-service time at moment:
Step 4: replacing the variable y in above formula with variable t, then obtain average life span are as follows:
2. a kind of rolling bearing life dynamic prediction method based on multiple features and phase space according to claim 1,
It is characterized in that, specific step is as follows for the third step:
Step 1: zero-mean processing, X are carried out to original matrixi=[xi1,xi2,…,xin]TFor i-th of relative characteristic index series,
Time domain and frequency domain character index is normalized and the original matrix of sliding treated relative characteristic index composition are as follows:
Step 2: carrying out linear transformation and obtain about X1,X2,…XpLinear combination:
Y1=a11X1+a12X2+…+a1pXp
Y2=a21X1+a22X2+…+a2pXp
Yp=ap1X1+ap2X2+…+appXp；
By linear transformation, a new coordinate system Y is obtained1,Y2,…,Yp, Y1,Y2,…,YpIt is the first, the of original variable
Two ..., pth principal component, and it is mutually irrelevant；I-th of principal component of original variable is with the covariance matrix of original matrix X
Ith feature value λiFeature vector (a after corresponding standardizationi1,ai2,…,aip) be coefficient linear combination, by eigenvalue λ by big
To minispread, the first, the second is obtained by linear combination ..., p-th of principal component；
Step 3: the life prediction using first principal component as the comprehensive performance indicator that fails, for rolling bearing.
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