CN106248381A - A kind of rolling bearing life dynamic prediction method based on multiple features and phase space - Google Patents

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, is standardized respectively processing with sliding obtaining relative characteristic index；Then utilize PCA technology that multiple characteristic indexs are merged, it is thus achieved that a comprehensive decline performance index series carries out biometry；Again the comprehensive decline performance indications of history degenerative process are carried out phase space reconfiguration, contrast with current degradation process in phase space, obtain the out-of-service time of a prediction；The out-of-service time finally this predicted and history out-of-service time coupling its probability density distribution of combinational estimation, calculate average life；And by analyze sample constantly accumulate expansion, obtaining the average life in different observation moment, the present invention can effectively reflect multifactorial effect in rolling bearing degenerative process, not retrained by assumed condition, reduce forecast error, it is achieved the life-span dynamically and is exactly predicted simultaneously.

Description

A kind of rolling bearing life dynamic prediction method based on multiple features and phase space

Technical field

The present invention relates to rolling bearing life electric powder prediction, be specifically related to a kind of based on multiple features with the rolling of phase space Dynamic bearing life-span dynamic prediction method.

Background technology

Rolling bearing is as one of parts important in plant equipment and flimsy critical component, and its performance is with reliable Property plays vital effect to performance and the reliability service of whole plant equipment.Rolling bearing life prediction is actually According to the degenerate state that it is current, it was predicted that its lost efficacy from bringing into operation to used by time, consequently facilitating in a planned way pacify Listing and indexing and repair, the maintenance decision for equipment lays the foundation.Therefore, it was predicted that the life-span of the rolling bearing precognition to equipment in running Keep in repair significant.

Choosing accurate predicted roll bearing life of performance indications is most important, and tradition biometry is with vibration signal One feature is predicted as decline performance indications, it is impossible to effectively reflect multifactorial work in rolling bearing degenerative process With.Owing to rolling bearing degenerative process has non-linear and non-stationary feature, tradition is by BP neutral net and supports vector Machine scheduling algorithm is set up Life Prediction Model and is carried out the method for biometry and retrained by assumed condition, and is subject in early days in prediction Observation sample quantity is few and the impact of random error, and the error that makes to predict the outcome is bigger, it is impossible to realize the accurate of rolling bearing life With dynamic prediction.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, it is an object of the invention to provide a kind of based on multiple features and phase space Rolling bearing life dynamic prediction method, it is possible to effectively multifactorial effect in reflection rolling bearing degenerative process, and not being subject to The constraint of assumed condition in biometry, decreases and is predicting what few by observation sample quantity in early days and random errors affect caused Forecast error, thus the life-span realizing rolling bearing dynamically and exactly predict.

To achieve these goals, the technical scheme that the present invention takes is:

A kind of rolling bearing life dynamic prediction method based on multiple features and phase space, comprises the following steps:

The first step, obtains the vibration signal of rolling bearing, extracts its multiple time domains and frequency domain character index；

Second step, is standardized time domain and frequency domain character index processing with sliding obtaining relative characteristic index respectively, Calculation procedure is as follows:

Step 1: arbitrarily choose the eigenvalue of one section of Trend Stationary in the normal phase, calculate the average of this section of eigenvalue；

Step 2: calculate primitive character value and the ratio of average, obtain a relative characteristic index；

Step 3: relative characteristic index is carried out M point sliding average treatment, M=5～20, x^RRXFor primitive character with average The ratio of number；x^MAFor the sequence after sliding is average, the most final relative characteristic index, computing formula is as follows:

$x_k^{MA}=\left\{\begin{array}{c}\frac{1}{k+3}\underset{i=1}{\overset{k+3}{\Σ}}{x}_i^{RRX},k\≤3\\ \frac{1}{7}\underset{i=k-3}{\overset{k+3}{\Σ}}{x}_i^{RRX},4\≤k\≤N-3\\ \frac{1}{N-k+4}\underset{i=k-3}{\overset{N}{\Σ}}{x}_i^{RRX},N-2\≤k\≤N\end{array}\right.;$

3rd step, utilizes PCA technology to merge multiple characteristic indexs, it is thus achieved that a comprehensive decline performance index series Carry out biometry；

The comprehensive decline performance indications of history degenerative process are carried out phase space reconfiguration by the 4th step, in phase space with work as Front degenerative process contrasts, and obtains the out-of-service time of a prediction；

5th step, the out-of-service time that this is predicted and history out-of-service time coupling its probability density distribution of combinational estimation, Calculate average life；

6th step, is constantly accumulated expansion and analyzes sample, obtain the average life in different observation moment by contraction time window.

Specifically comprising the following steps that of the 3rd described step

Step 1: original matrix is carried out zero-mean process, X_i=[x_i1,x_i2,…,x_in]^TFor i-th relative characteristic index Sequence, time domain and frequency domain character index be normalized and sliding process after the original matrix of relative characteristic index composition be:

$X={(X_1,X_2,\mathrm{...},X_p)}^T=\left\{\begin{array}{cccc}{x}_{11}& x_{12}& \mathrm{...}& x_{1n}\\ x_{21}& x_{22}& \mathrm{...}& x_{2n}\\ & & & .\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& .\\ & & & .\\ x_{p1}& x_{p2}& \mathrm{...}& x_{pn}\end{array}\right\};$

Step 2: carry out linear transformation and obtain about X₁,X₂,…X_pLinear combination:

Y₁=a₁₁X₁+a₁₂X₂+…+a_1pX_p

Y₂=a₂₁X₁+a₂₂X₂+…+a_2pX_p

Y_p=a_p1X₁+a_p2X₂+…+a_ppX_p；

By linear transformation, obtain new coordinate system Y₁,Y₂,…,Y_p, Y₁,Y₂,…,Y_pFor the first of original variable, Second ..., pth main constituent, and mutually orthogonal；The i-th main constituent of original variable is with the covariance matrix of original matrix X Ith feature value λ_iCharacteristic vector (a after corresponding standardization_i1,a_i2,…,a_ip) be the linear combination of coefficient, by eigenvalue λ by Greatly to minispread, obtain first by linear combination, second ..., pth main constituent；

Step 3: using first principal component as the performance indications that comprehensively fail, for the biometry of rolling bearing.

The detailed process of the 4th described step is:

Step 1: assume the comprehensive decline performance index series having M group history degenerative process, these index series are carried out Phase space reconfiguration, it is achieved the kinetics track of rolling bearing degenerative process is fully deployed in phase space；

Step 2: the study of Degradation path function in phase space, utilizes radial direction base (RBF) neutral net to nonlinear function Excellent approximation capability obtains nonlinear loci function, realizes of Degradation path function in phase space by RBF neural Practise；

The comprehensive decline performance index series assuming i-th group of history degenerative process is X_i={ x_i(t₁),x_i(t₂),…,x_i (t_n), wherein i=1,2 ..., M, n are the length of i-th group of index series, k=1,2 ... L.L=n-(m_i-1)τ_iThrough empty mutually Between reconstruct after vector be:

xx_ik(t)={ x_i(t_k),x_i(t_k+τ_i),…,x_i(t_k+(m_i-1)τ_i)}

By the vector { xx after reconstruct_ik(t) | k=1,2 ..., L} and corresponding active time { t_k| k=1,2 ..., L} divides Do not carry out the training of RBF neural as input and output, obtain the trajectory of phase space function of i-th group of history degenerative process, Other each group history degenerative processes all experience identical training and obtain different lopcus functions；

Step 3: prediction out-of-service time, it is assumed that the degenerative process being currently needed for prediction is the M+1 time degenerative process, at this Observation the moment be predicted correspondence the operation time be T_M+1, the comprehensive decline performance index series of foundation is { x_M+1(t₁),x_M+1 (t₂),…,x_M+1(t_n), this sequence is carried out phase space reconfiguration, reconstructed vector is input to the RBF after having trained through network In learn, it is thus achieved that one group estimate operation time arrow [T₁,T₂,…T_M], calculate this operation time and actual run time Deviation:

e_i=(T_i-T_M+1)²I=1,2 ... M

Then at moment T_M+1Place obtains an error vector e=[e₁,e₂,…,e_M], thus obtain this moment Degradation path with The similarity degree of history Degradation path:

$W_i=\frac{1/e_i}{\underset{i=1}{\overset{M}{\Σ}}1/e_i},i=1,2,\mathrm{...},M$

t_M+1For the out-of-service time of current time prediction, t_iFor rolling bearing history service life, according to similarity degree with go through The measurable rolling bearing of history service life is in the out-of-service time of current time:

$t_{M+1}=\underset{i=1}{\overset{M}{\Σ}}{W}_i{t}_i$

Upper once predict time, by telescopic window expand performance indications data, repeat above step and obtain a new mistake Difference vector, is added new error vector with the error vector of last computation and is again assigned to new error vector.

The detailed process of the 5th described step is:

Step 1: input sample data, carries out the out-of-service time of history out-of-service time and current predictive mating as input Sample, it is assumed that current predictive is when kth is observed, and the sample set obtained isWherein m is sample point Number；

Step 2: exptended sample, is originally inputted sample X_kNew sample Y is obtained by RBF neural after being expanded_k={ y₁, y₂,…,y_n, wherein n is sample points after expanding, and n ＞ m；

Step 3: probability Estimation, σ is smoothing factor, after data normalizationCuclear density method is used to estimate this The probability density distribution of observation out-of-service time in moment:

$R\left(y\right)=\frac{1}{n\mathrm{\σ}\sqrt{2\mathrm{\π}}}\underset{i=1}{\overset{n}{\Σ}}\exp (-\frac{{(y-y_i)}^2}{2{\mathrm{\σ}}^2});$

Step 4: replace the variable y in above formula with variable t, then obtaining average life is:

$u=\underset{0}{\overset{\mathrm{\∞}}{\∫}}tR\left(t\right)dt.$

Advantages of the present invention is:

1. by PCA technology establish one more effectively, more comprehensively react rolling bearing degradation information comprehensive degenerative Index can carry out biometry.

2. achieve history Degradation path and the contrast of current degradation track by phase space reconstruction technique, not by the life-span pre- The constraint of assumed condition in survey.

3., by estimating the probability density distribution of rolling bearing out-of-service time, it is achieved that the estimation of average life, decrease By the forecast error that observation sample produces less in early days, and predict the outcome along with the accumulation dynamic of observation sample updates, improve pre- The accuracy surveyed.

Accompanying drawing explanation

Fig. 1 is the flow chart of the embodiment of the present invention.

Fig. 2 is that the comprehensive decline performance indications of embodiment 6 groups training rolling bearing change over curve chart.

Fig. 3 is that the comprehensive decline performance indications of tested rolling bearing change over curve chart.

Fig. 4 is the comparison diagram of current degradation process and history degenerative process.

Fig. 5 is the dynamic probability model figure of out-of-service time.

Detailed description of the invention

The present invention is described in detail with embodiment below in conjunction with the accompanying drawings.

With reference to Fig. 1, a kind of rolling bearing life dynamic prediction method based on multiple features and phase space, including following step 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 Shown in, x={x₁,x₂,…,x_NIt is vibration signal,

Table 1 has dimension time domain index

Table 2 non_dimensional time domain index

In frequency-domain index calculates, s (k) is the frequency spectrum of signal x, k=1,2 ..., K, K are spectral line number, f_kIt it is kth bar spectrum The frequency values of line,

Table 3 frequency-domain index

Second step, in order to reduce the difference between different bearing, is standardized respectively by time domain and frequency domain character index Processing with sliding and obtain relative characteristic index, calculation procedure is as follows:

Step 1: arbitrarily choose the eigenvalue of one section of Trend Stationary in the normal phase, calculate the average of this section of eigenvalue；

Step 2: calculate primitive character value and the ratio of average, obtain a relative characteristic index；

Step 3: relative characteristic index above is carried out M point sliding average treatment, M=5～20, x^RRXFor primitive character Ratio with average；x^MAFor the sequence after sliding is average, the most final relative characteristic index, computing formula is as follows:

$x_k^{MA}=\left\{\begin{array}{c}\frac{1}{k+3}\underset{i=1}{\overset{k+3}{\Σ}}{x}_i^{RRX},k\≤3\\ \frac{1}{7}\underset{i=k-3}{\overset{k+3}{\Σ}}{x}_i^{RRX},4\≤k\≤N-3\\ \frac{1}{N-k+4}\underset{i=k-3}{\overset{N}{\Σ}}{x}_i^{RRX},N-2\≤k\≤N\end{array}\right.;$

3rd step, utilizes PCA technology to merge multiple characteristic indexs, it is thus achieved that one can more effectively be reacted rolling bearing The comprehensive decline performance index series of degenerative process carries out biometry, specifically comprises the following steps that

Step 1: original matrix is carried out zero-mean process, X_i=[x_i1,x_i2,…,x_in]^TFor i-th relative characteristic index Sequence, time domain and frequency domain character index be normalized and sliding process after the original matrix of relative characteristic index composition be:

$X={(X_1,X_2,\mathrm{...},X_p)}^T=\left\{\begin{array}{cccc}{x}_{11}& x_{12}& \mathrm{...}& x_{1n}\\ x_{21}& x_{22}& \mathrm{...}& x_{2n}\\ & & & .\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& .\\ & & & .\\ x_{p1}& x_{p2}& \mathrm{...}& x_{pn}\end{array}\right\};$

Step 2: carry out linear transformation and obtain about X₁,X₂,…X_pLinear combination:

Y₁=a₁₁X₁+a₁₂X₂+…+a_1pX_p

Y₂=a₂₁X₁+a₂₂X₂+…+a_2pX_p

Y_p=a_p1X₁+a_p2X₂+…+a_ppX_p；

By linear transformation, obtain new coordinate system Y₁,Y₂,…,Y_p, Y₁,Y₂,…,Y_pFor the first of original variable, Second ..., pth main constituent, and mutually orthogonal；The i-th main constituent of original variable is with the covariance matrix of original matrix X Ith feature value λ_iCharacteristic vector (a after corresponding standardization_i1,a_i2,…,a_ip) be the linear combination of coefficient, by eigenvalue λ by Greatly to minispread, obtain first by linear combination, second ..., pth main constituent；

Step 3: using first principal component as the performance indications that comprehensively fail, for the biometry of rolling bearing；With reference to Fig. 2 With the comprehensive decline performance indications that Fig. 3, Fig. 2 are 6 groups of training rolling bearings change over curve chart, Fig. 3 is predicted roll axle The comprehensive decline performance indications held change over curve chart；

The comprehensive decline performance indications of history degenerative process are carried out phase space reconfiguration by the 4th step, in phase space with work as Front degenerative process contrasts, and obtains the out-of-service time of a prediction, and flow 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 is X={x (t₁),x (t₂),…,x(t_n), if m and τ is Embedded dimensions and the time delay of this sequence, therefore, phase space can produce L embedding Point, L=n-(m-1) τ, wherein (m-1) τ is the time delay window of this sequence；

According to time delay thought, the phase space vector such as following formula after time series reconstruct, wherein xx_kT () is phase space In a point:

xx_k(t)=[x (t_k),x(t_k+τ),…,x(t_k+ (m-1) τ)], k=1,2 ..., L

Rolling bearing history degenerative process has important reference value, therefore to the prediction currently experiencing similar process Set up 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 contrasts, and detailed process is as follows:

Step 1: assume the comprehensive decline performance index series having M group history degenerative process, these index series are carried out Phase space reconfiguration, it is achieved the kinetics 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 Can not directly give, but utilize radially base (RBF) neutral net that the approximation capability that nonlinear function is excellent is obtained non-linear rail Trace function, i.e. realizes the study of Degradation path function in phase space by RBF neural；

The quantity of neutral net is to be determined by the quantity of history degenerative process, it is assumed that i-th group of history degenerative process comprehensive Decline performance index series is X_i={ x_i(t₁),x_i(t₂),…,x_i(t_n), wherein i=1,2 ..., M, n are i-th group of index sequence The length of row, k=1,2 ... L.L=n-(m_i-1)τ_iAfter phase space reconfiguration, vector is:

xx_ik(t)={ x_i(t_k),x_i(t_k+τ_i),…,x_i(t_k+(m_i-1)τ_i)}

By the vector { xx after reconstruct_ik(t) | k=1,2 ..., L} and corresponding active time { t_k| k=1,2 ..., L} divides Do not carry out the training of RBF neural as input and output, obtain the trajectory of phase space function of i-th group of history degenerative process, Other each group history degenerative processes all experience identical training and obtain different lopcus functions；

Step 3: prediction out-of-service time, it is assumed that the degenerative process being currently needed for prediction is the M+1 time degenerative process, at this Observation the moment be predicted correspondence the operation time be T_M+1, the comprehensive decline performance index series of foundation is { x_M+1(t₁),x_M+1 (t₂),…,x_M+1(t_n), this sequence is carried out phase space reconfiguration, reconstructed vector is input to the RBF after having trained through network In learn, it is thus achieved that one group estimate operation time arrow [T₁,T₂,…T_M], calculate this operation time and actual run time Deviation:

e_i=(T_i-T_M+1)²I=1,2 ... M

Then at moment T_M+1Place obtains an error vector e=[e₁,e₂,…,e_M], thus obtain this moment Degradation path with The similarity degree of history Degradation path:

$W_i=\frac{1/e_i}{\underset{i=1}{\overset{M}{\Σ}}1/e_i},i=1,2,\mathrm{...},M$

t_M+1For the out-of-service time of current time prediction, t_iFor rolling bearing history service life, according to similarity degree with go through The measurable rolling bearing of history service life is in the out-of-service time of current time:

$t_{M+1}=\underset{i=1}{\overset{M}{\Σ}}{W}_i{t}_i$

Upper once predict time, by telescopic window expand performance indications data, repeat above step and obtain a new mistake Difference vector, in order to reduce the exceptional data point impact on predicting the outcome, by the error vector phase of new error vector with last computation Add and be again assigned to new error vector；

5th step, the out-of-service time that this is predicted and history out-of-service time coupling its probability density distribution of combinational estimation, Calculate average life, as shown in Figure 5；

In rolling bearing life prediction in early days, affected with system noise owing to being lacked by observation data, it was predicted that inefficacy Time and actual value deviation are relatively big, therefore, in order to improve the accuracy of prediction, eliminate the impact of various random factor, and will be current The out-of-service time of prediction and history degradation failure time, as statistical sample, estimate its probability density distribution, calculate average life Predicting the outcome as current time, detailed process is as follows:

Step 1: input sample data, carries out the out-of-service time of history out-of-service time and current predictive mating as input Sample, it is assumed that current predictive is when kth is observed, and the sample set obtained isWherein m is sample point Number；

Step 2: exptended sample, is originally inputted sample X_kNew sample Y is obtained by RBF neural after being expanded_k={ y₁, y₂,…,y_n, wherein n is sample points after expanding, and n ＞ m；

Step 3: probability Estimation, σ is smoothing factor, after data normalizationCuclear density method is used to estimate this The probability density distribution of observation out-of-service time in moment:

$R\left(y\right)=\frac{1}{n\mathrm{\σ}\sqrt{2\mathrm{\π}}}\underset{i=1}{\overset{n}{\Σ}}\exp (-\frac{{(y-y_i)}^2}{2{\mathrm{\σ}}^2});$

Step 4: replace the variable y in above formula with variable t, then obtaining average life is:

$u=\underset{0}{\overset{\mathrm{\∞}}{\∫}}tR\left(t\right)dt;$

6th step, is constantly accumulated expansion and analyzes sample, obtain the average life in different observation moment by contraction time window, As shown in table 4.

The average life of table 4 rolling bearing prediction

Claims (4)

1. a rolling bearing life dynamic prediction method based on multiple features and phase space, it is characterised in that include following step Rapid:

The first step, obtains the vibration signal of rolling bearing, extracts its multiple time domains and frequency domain character index；

Second step, is standardized time domain and frequency domain character index respectively processing with sliding obtaining relative characteristic index, calculates Step is as follows:

Step 1: arbitrarily choose the eigenvalue of one section of Trend Stationary in the normal phase, calculate the average of this section of eigenvalue；

Step 2: calculate primitive character value and the ratio of average, obtain a relative characteristic index；

Step 3: relative characteristic index is carried out M point sliding average treatment, M=5～20, x^RRXFor primitive character and average Ratio；x^MAFor the sequence after sliding is average, the most final relative characteristic index, computing formula is as follows:

$x_k^{MA}=\left\{\begin{array}{c}\frac{1}{k+3}\underset{i=1}{\overset{k+3}{\mathrm{\Σ}}}{x}_i^{RRX},k\≤3\\ \frac{1}{7}\underset{i=k-3}{\overset{k+3}{\mathrm{\Σ}}}{x}_i^{RRX},4\≤k\≤N-3\\ \frac{1}{N-k+4}\underset{i=k-3}{\overset{N}{\mathrm{\Σ}}}{x}_i^{RRX},N-2\≤k\≤N\end{array}\right.;$

3rd step, utilizes PCA technology to merge multiple characteristic indexs, it is thus achieved that a comprehensive decline performance index series is carried out Biometry；

The comprehensive decline performance indications of history degenerative process are carried out phase space reconfiguration by the 4th step, in phase space with currently move back Change process contrasts, and obtains the out-of-service time of a prediction；

5th step, the out-of-service time this predicted and history out-of-service time coupling its probability density distribution of combinational estimation, calculate Average life；

6th step, is constantly accumulated expansion and analyzes sample, obtain the average life in different observation moment by contraction time window.

A kind of rolling bearing life dynamic prediction method based on multiple features and phase space the most according to claim 1, its It is characterised by, specifically comprising the following steps that of the 3rd described step

Step 1: original matrix is carried out zero-mean process, X_i=[x_i1,x_i2,…,x_in]^TFor i-th relative characteristic index series, Time domain and frequency domain character index is normalized and sliding process after the original matrix of relative characteristic index composition be:

$X={(X_1,X_2,...,X_p)}^T=\left\{\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1n}\\ x_{21}& x_{22}& ...& x_{2n}\\ \begin{array}{c}\\ ...\\ \end{array}& \begin{array}{c}\\ ...\\ \end{array}& \begin{array}{c}\\ ...\\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ x_{p1}& x_{p2}& ...& x_{pn}\end{array}\right\};$

Step 2: carry out linear transformation and obtain about X₁,X₂,…X_pLinear combination:

$\begin{array}{c}{Y}_1=a_{11}{X}_1+a_{12}{X}_2+...+a_{1p}{X}_p\\ Y_2=a_{21}{X}_1+a_{22}{X}_2+...+a_{2p}{X}_p\\ \begin{array}{c}.\\ .\\ .\end{array}\\ Y_p=a_{p1}{X}_1+a_{p2}{X}_2+...+a_{pp}{X}_p\end{array};$

By linear transformation, obtain new coordinate system Y₁,Y₂,…,Y_p, Y₁,Y₂,…,Y_pFor original variable the first, the Two ..., pth main constituent, and mutually orthogonal；The i-th main constituent of original variable is with the covariance matrix of original matrix X Ith feature value λ_iCharacteristic vector (a after corresponding standardization_i1,a_i2,…,a_ip) it is the linear combination of coefficient, by eigenvalue λ by greatly To minispread, obtain first by linear combination, second ..., pth main constituent；

Step 3: using first principal component as the performance indications that comprehensively fail, for the biometry of rolling bearing.

A kind of rolling bearing life dynamic prediction method based on multiple features and phase space the most according to claim 1, its Being characterised by, the detailed process of the 4th described step is:

Step 1: assume the comprehensive decline performance index series having M group history degenerative process, these index series are carried out empty mutually Between reconstruct, it is achieved the kinetics track of rolling bearing degenerative process is fully deployed in phase space；

Step 2: the study of Degradation path function in phase space, utilizes radially base (RBF) neutral net excellent to nonlinear function Approximation capability obtain nonlinear loci function, realize the study of Degradation path function in phase space by RBF neural；

The comprehensive decline performance index series assuming i-th group of history degenerative process is X_i={ x_i(t₁),x_i(t₂),…,x_i(t_n), Wherein i=1,2 ..., M, n are the length of i-th group of index series, k=1,2 ... L. L=n-(m_i-1)τ_iThrough phase space reconfiguration Rear vector is:

xx_ik(t)={ x_i(t_k),x_i(t_k+τ_i),…,x_i(t_k+(m_i-1)τ_i)}

By the vector { xx after reconstruct_ik(t) | k=1,2 ..., L} and corresponding active time { t_k| k=1,2 ..., L} makees respectively Carry out the training of RBF neural for input and output, obtain the trajectory of phase space function of i-th group of history degenerative process, other Each group history degenerative process all experiences identical training and obtains different lopcus functions；

Step 3: prediction out-of-service time, it is assumed that the degenerative process being currently needed for prediction is the M+1 time degenerative process, in this observation Moment be predicted correspondence the operation time be T_M+1, the comprehensive decline performance index series of foundation is { x_M+1(t₁),x_M+1 (t₂),…,x_M+1(t_n), this sequence is carried out phase space reconfiguration, reconstructed vector is input to the RBF after having trained through network In learn, it is thus achieved that one group estimate operation time arrow [T₁,T₂,…T_M], calculate this operation time and actual run time Deviation:

e_i=(T_i-T_M+1)²I=1,2 ... M

Then at moment T_M+1Place obtains an error vector e=[e₁,e₂,…,e_M], thus obtain this moment Degradation path and history The similarity degree of Degradation path:

$W_i=\frac{1/e_i}{\underset{i=1}{\overset{M}{\Σ}}1/e_i},i=1,2,...,M$

t_M+1For the out-of-service time of current time prediction, t_iFor rolling bearing history service life, take according to similarity degree and history Labour life-span measurable rolling bearing is in the out-of-service time of current time:

$t_{M+1}=\underset{i=1}{\overset{M}{\Σ}}{W}_i{t}_i$

Upper once predict time, by telescopic window expand performance indications data, repeat above step obtain a new error to Amount, is added new error vector with the error vector of last computation and is again assigned to new error vector.

A kind of rolling bearing life dynamic prediction method based on multiple features and phase space the most according to claim 1, its Being characterised by, the detailed process of the 5th described step is:

Step 1: input sample data, carries out the out-of-service time of history out-of-service time and current predictive mating as input sample This, it is assumed that current predictive is when kth is observed, and the sample set obtained isWherein m is sample point Number；

Step 2: exptended sample, is originally inputted sample X_kNew sample Y is obtained by RBF neural after being expanded_k={ y₁, y₂,…,y_n, wherein n is sample points after expanding, and n ＞ m；

Step 3: probability Estimation, σ is smoothing factor, after data normalizationCuclear density method is used to estimate this observation The probability density distribution of out-of-service time in moment:

$R\left(y\right)=\frac{1}{n\mathrm{\σ}\sqrt{2\mathrm{\π}}}\underset{i=1}{\overset{n}{\Σ}}\exp (-\frac{{(y-y_i)}^2}{2{\mathrm{\σ}}^2});$

Step 4: replace the variable y in above formula with variable t, then obtaining average life is:

$u=\underset{0}{\overset{\mathrm{\∞}}{\∫}}tR\left(t\right)dt.$