CN102831325B - A kind of bearing fault Forecasting Methodology returned based on Gaussian process - Google Patents

A kind of bearing fault Forecasting Methodology returned based on Gaussian process Download PDF

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CN102831325B
CN102831325B CN201210323398.3A CN201210323398A CN102831325B CN 102831325 B CN102831325 B CN 102831325B CN 201210323398 A CN201210323398 A CN 201210323398A CN 102831325 B CN102831325 B CN 102831325B
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bearing
gaussian
parameter
vibration signal
carries
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CN102831325A (en
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洪晟
周正
杨洪旗
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北京航空航天大学
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Abstract

Based on the bearing fault Forecasting Methodology that Gaussian process returns, it has five large steps: step one, and setting prognoses system parameter, carries out initialization to Gaussian process regression model; Step 2, taken at regular intervals bearing vibration signal, carries out to vibration signal the time domain charactreristic parameter that feature extraction obtains bearing vibration signal, carries out failure symptom judgement; Step 3, judges whether the sign that breaks down; Step 4, the calculating of characteristic parameter and storage, and carry out dynamically updating of Gaussian process regression model; Step 5, carries out the failure prediction of bearing.The present invention is according to the actual service condition of product, gather low volume data, provide to quantification the time that product may break down, use Gaussian process to return and improve arithmetic speed and precision of prediction, use the thought of health control, the life cycle management of bearing is divided into health, inferior health, three time periods of fault, in sub-health state, carries out failure prediction, improve bearing use management ability.

Description

A kind of bearing fault Forecasting Methodology returned based on Gaussian process
Technical field:
The present invention relates to a kind of bearing fault Forecasting Methodology returned based on Gaussian process, belong to bearing fault electric powder prediction.
Background technology:
Bearing is the indispensable parts of rotating machinery, ensure the kernel component of the important equipment facility precision such as precision machine tool, high-speed railway, aerogenerator, performance, life and reliability especially, bearing belongs to fragile part simultaneously, and therefore its status monitoring, fault diagnosis, failure prediction are study hotspots always.In recent years, the condition maintenarnce of system is subject to people's attention gradually, failure prediction technology as the core technology of condition based maintenance for raising production safety, reduce production cost and extension device serviceable life, be all significant.
At present in the failure prediction of bearing, the feature extraction usual way of vibration signal selects Time-domain Statistics amount as life characteristics parameter.The temporal signatures information of the vibration signal of bearing own, as root-mean-square value, peak value, shape factor, peak factor etc. can change along with bearing fault.By judging and predicting that the analog value whether these time domain parameter values are greater than normal bearing judges whether to there is fault.Different magnitude parameters is different to different Fault-Sensitive degree, and such as root-mean-square value is to wearing and tearing class Fault-Sensitive, and peak index peels off for element surface, impression Fault-Sensitive, and peak factor can judge two class faults.There are statistics to show, use kurtosis coefficient and effective value jointly to monitor the Vibration Condition of rolling bearing, to the rate of accuracy reached more than 95% that rolling bearing fault judges.Although magnitude parameters method can not the position of alignment bearing fault, and method is simple and can characterize fault progression trend preferably.
Domestic existing scholar utilizes Grey System Method, blur method and maximum entropy method etc. to predict bearing fault.Bear vibration has non-linear and feature that is ambiguity, not easily sets up accurate mathematical model.And the fault of bearing has individual otherness, and different with the fault mode of appearance in the life-span of different operating mode lower bearing reality, existing method can not address this problem well.In addition, existing method, as neural network etc., precision of prediction, consuming time etc. in performance not fully up to expectations.
Summary of the invention:
The present invention is directed to deficiency of the prior art and demand, propose a kind of bearing fault Forecasting Methodology returned based on Gaussian process.The vibration signal of its timing acquiring bearing, is analyzed and feature extraction by time domain parameter, obtains the characteristic parameter of bearing vibration signal, according to the threshold value of setting, is divided into health, inferior health, three periods of fault the bearing life cycle.When bearing enters sub-health state, calculate according to vibration signal and store characteristic parameter (as mean square value and kurtosis value etc.), adopting Gaussian process homing method to carry out failure prediction respectively.When there being new data to arrive, carry out feature extraction and be input in forecast model, dynamically update the parameter of model, acquisition predicts the outcome.
A kind of bearing fault Forecasting Methodology returned based on Gaussian process of the present invention, it step comprised is as follows:
Step one, setting prognoses system parameter, Gaussian process regression model carries out initialization.
Setting prognoses system decision threshold 1, decision threshold 2.When the characteristic parameter predicted is higher than decision threshold 1, judge that bearing enters sub-health state, application Gaussian process regression model carries out failure prediction; When the characteristic parameter predicted is higher than decision threshold 2, judge that bearing is by fault, should give maintain and replace.
The setting vibration signals collecting cycle.Should not be too short in the health status down-sampling cycle, after entering sub-health state, reduce the sampling period.In general, for the bearing in continuous firing, under health status, every day samples 1 time, each 1s, and sampling rate can be set to 20kHz; Sampling in every 30 minutes 1 time under sub-health state, each 1s, sampling rate can be set to 20kHz.
It is a kind of core learning machine algorithm that Gaussian process returns, and should carry out choosing and the setting of hyper parameter initial value of kernel function, and hyper parameter initial searching region can rule of thumb free setting, and hyper parameter initial value can be set to zero, is learnt to obtain by Algorithm for Training.Conventional kernel function has SE core, NN core, Matern core etc.
SE kernel function: C SE ( x , x ′ ) = σ f 2 exp ( - P ( x , x ′ ) 2 2 )
NN kernel function: C NN ( x , x ′ ) = σ f 2 sin - 1 ( 2 x ~ T Σ x ~ ′ ( 1 + 2 x ~ T Σ x ~ ) ( 1 + 2 x ~ ′ Σ x ~ ′ ) )
Matern kernel function: C Matern ( r ) = 2 1 - v Γ ( v ) ( 2 v r l ) v K v ( 2 v r l )
In formula, symbol description is as follows: order for comprising the vector of all hyper parameter, { P}=1 -2i represents hyper parameter l -2with the product matrix of I; for the signal variance of kernel function, the degree of controls local correlativity. for the augmented matrix of x, namely v, l are parameter, K vmodified Bessel function, v can value be 1/2,3/2,5/2 etc.
Step 2, taken at regular intervals bearing vibration signal, carries out to vibration signal the time domain charactreristic parameter that feature extraction obtains bearing vibration signal, carries out failure symptom judgement.
Carry out the collection of vibration signal according to the sampling period of setting, and carry out the feature extraction of time domain charactreristic parameter.Carry out the most frequently used dimension index that has of process to bearing vibration signal and comprise root-mean-square value (RMS) and peak value (PEAK), dimensionless index height expands shape factor S, peak factor C, pulse factor I, nargin factor L, kurtosis index K etc.This method is using root-mean-square value and kurtosis index as the parameter of failure prediction.
Root-mean-square value (RMS) can measure the vibratory output of bearing, has both considered the experience process that time of vibration changes, and indicates again the size of mechanical vibrational energy simultaneously.Because root-mean-square value is average to the time, so can as appropriate evaluation to having the wearing and tearing class faults such as surface crack.The computing formula of root-mean-square value is as follows:
RMS = Σ k = 1 K ( x ( k ) ) 2 K
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used.
Kurtosis index (Kurtosis) is the tolerance of the high and steep degree of probability density distribution point, represents in vibrational waveform whether have impact or sharp high and steep degree.Kurtosis index is more responsive for shock pulse class failure ratio, and when particularly fault is early stage, they have obvious increase.The computing formula of kurtosis index is as follows:
Kurtosis = Σ k = 1 K ( x ( k ) - x m ) 4 K x std 4
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used; x mfor signal average, x stdfor signal standards is poor, wherein x mand x stdcomputing formula as follows:
x m = 1 K Σ K = 1 K x ( k )
x std = Σ k = 1 K ( x ( k ) - x m ) 2 K - 1
Calculate vibration signal root-mean-square value and kurtosis index respectively, compare with inferior health decision threshold 1, namely think occurred minor failure sign if these two characteristic parameters have one to exceed setting threshold value, bearing enters sub-health state.
Step 3, judges whether the sign that breaks down.
After judgement bearing enters sub-health state, reduce the sampling period of vibration signal, start Gaussian process regression model, carry out failure prediction, proceed to step 4.
When judgement bearing working is normal, when not entering sub-health state, keep current state, return step 2 and continue monitoring vibration signal.
Step 4, the calculating of characteristic parameter and storage, and carry out dynamically updating of Gaussian process regression model.
Calculate vibration signal root-mean-square value and kurtosis index respectively, and these two kinds of characteristic parameters are stored respectively.The characteristic parameter obtained by current time and the characteristic parameter obtained in front several time period, be integrated into Gaussian process regression model input vector, input in this forecast model.
When there being the new vibration signal gathered to arrive, calculating and storing characteristic parameter, and integrating new input vector, upgrade Gaussian process regression model.
Step 5, carries out the failure prediction of bearing.
Application Gaussian process regression model adopts Gaussian process homing method to train to input vector, carries out the root-mean-square value of vibration signal and the trend analysis of kurtosis index two kinds of characteristic parameters, draws failure prediction result and fiducial interval distribution.The fault that two kinds of parameter characterizations are dissimilar.Gained predicts the outcome and should carry out predicting that the minimum value of acquired results is as the criterion with two kinds of characteristic parameters.
A kind of bearing fault Forecasting Methodology returned based on Gaussian process of the present invention, it has following advantage and good effect:
1) method provided by the invention is according to the actual service condition of product, gathers low volume data, provides to quantification the time that product may break down.Use Gaussian process to return and improve arithmetic speed and precision of prediction.Use the thought of health control, the life cycle management of bearing is divided into health, inferior health, three time periods of fault, in sub-health state, carries out failure prediction, improve bearing use management ability.
2) compared with the conventional method, provided by the present inventionly return the method for carrying out bearing fault prediction based on Gaussian process there is quantification, simple and quick advantage, the fiducial interval of prediction is provided simultaneously, make to predict the outcome more accurate.More applicable with impact class bearing fault to wearing and tearing class.
Accompanying drawing illustrates:
The process flow diagram of the bearing fault Forecasting Methodology that Fig. 1 returns based on Gaussian process
Embodiment:
Below in conjunction with accompanying drawing, technical scheme of the present invention is described further.
See Fig. 1, the present invention, a kind of bearing fault Forecasting Methodology returned based on Gaussian process, the method concrete steps are as follows:
Step one, setting prognoses system parameter, Gaussian process regression model carries out initialization.
Setting prognoses system decision threshold 1, decision threshold 2.When characteristic parameter is higher than decision threshold 1, judge that bearing enters sub-health state, application and trouble forecast model carries out failure prediction; When the characteristic parameter predicted reaches decision threshold 2, judge that bearing is by fault, should give maintain and replace.
The setting of decision threshold should by studying and combining experience setting in the past voluntarily.For there being dimension index (as root-mean-square value), its numerical value is different for different bearing, should carry out Primary Study and obtain normal value.When being set as decision threshold 1 with during normal value deviation 5%, when being set as decision threshold 2 with during normal value deviation 20%.For dimensionless index (as kurtosis index), its to the operating condition of machine irrelevant (namely to amplitude and frequency insensitive), only depend on the amplitude probability density function of signal.The kurtosis index of health status lower bearing is generally 3 ~ 4, namely illustrates to there is impact vibration, be set as decision threshold 1 more than 5; Violent in the kurtosis index change of later stage in inferior health stage, can think that bearing enters failure phase, be set as decision threshold 2.
The setting vibration signals collecting cycle.Should not be too short in the health status down-sampling cycle, after entering sub-health state, reduce the sampling period.In general, for the bearing in continuous firing, under health status, every day samples 1 time, each 1s, and sampling rate can be set to 20kHz; Sampling in every 30 minutes 1 time under sub-health state, each 1s, sampling rate can be set to 20kHz.The acquisition method of vibration signal and the setting of collection period can be obtained by the document delivered, report, handbook.
The initial parameter of setting Gaussian process regressive prediction model.It is a kind of core learning machine algorithm that Gaussian process returns, and should carry out choosing of kernel function and set with hyper parameter initial value.The principle of Gaussian process regression algorithm and realize to be obtained by the document delivered, books.Conventional kernel function has a square index (SE) kernel function, neural network (NN) kernel function, Matern class kernel function etc.
SE kernel function: C SE ( x , x ′ ) = σ f 2 exp ( - P ( x , x ′ ) 2 2 )
NN kernel function: C NN ( x , x ′ ) = σ f 2 sin - 1 ( 2 x ~ T Σ x ~ ′ ( 1 + 2 x ~ T Σ x ~ ) ( 1 + 2 x ~ ′ Σ x ~ ′ ) )
Matern kernel function: C Matern ( r ) = 2 1 - v Γ ( v ) ( 2 v r l ) v K v ( 2 v r l )
In formula, symbol description is as follows: order for comprising the vector of all hyper parameter, { P}=1 -2i represents hyper parameter 1 -2with the product matrix of I; for the signal variance of kernel function, the degree of controls local correlativity. for the augmented matrix of x, namely v, l are parameter, K vmodified Bessel function, v can value be 1/2,3/2,5/2 etc.
Step 2, taken at regular intervals bearing vibration signal, carries out to vibration signal the time domain charactreristic parameter that feature extraction obtains bearing vibration signal, carries out failure symptom judgement.
Carry out the collection of vibration signal according to the sampling period of setting, and carry out the feature extraction of time domain charactreristic parameter.Carry out the most frequently used dimension index that has of process to bearing vibration signal and comprise root-mean-square value (RMS) and peak value (PEAK), dimensionless index height expands shape factor S, peak factor C, pulse factor I, nargin factor L, kurtosis index K etc.Root-mean-square value can Efficient Characterization wearing and tearing class fault, and kurtosis index can impact class fault by Efficient Characterization, and this method is using root-mean-square value and kurtosis index as the parameter of failure prediction.
Root-mean-square value (RMS) can measure the vibratory output of bearing, has both considered the experience process that time of vibration changes, and indicates again the size of mechanical vibrational energy simultaneously.Because root-mean-square value is average to the time, so can as appropriate evaluation to having the wearing and tearing class faults such as surface crack.The computing formula of root-mean-square value is as follows:
RMS = Σ k = 1 K ( x ( k ) ) 2 K
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used.
Kurtosis index (Kurtosis) is the tolerance of the high and steep degree of probability density distribution point, represents in vibrational waveform whether have impact or sharp high and steep degree.Kurtosis index is more responsive for shock pulse class failure ratio, and when particularly fault is early stage, they have obvious increase.The computing formula of kurtosis index is as follows:
Kurtosis = Σ k = 1 K ( x ( k ) - x m ) 4 K x std 4
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used; x mfor signal average, x stdfor signal standards is poor, wherein x mand x stdcomputing formula as follows:
x m = 1 K Σ K = 1 K x ( k )
x std = Σ k = 1 K ( x ( k ) - x m ) 2 K - 1
Calculate vibration signal root-mean-square value and kurtosis index respectively, compare with inferior health decision threshold 1, namely think occurred minor failure sign if these two characteristic parameters have one to exceed setting threshold value, bearing enters sub-health state.
Step 3, judges whether the sign that breaks down.
After judgement bearing enters sub-health state, reduce the sampling period of vibration signal, start Gaussian process and return failure prediction model, carry out failure prediction, proceed to step 4.
When judgement bearing working is normal, when not entering sub-health state, keep current state, return step 2, continue monitoring vibration signal.
Step 4, the calculating of characteristic parameter and storage, and carry out dynamically updating of Gaussian process regressive prediction model.
Calculate vibration signal root-mean-square value and kurtosis index respectively, these two kinds of characteristic parameters with formula used in step 2, and store by computing method respectively.The characteristic parameter obtained by current time and the characteristic parameter obtained in front several time period, be integrated into forecast model input vector, input in forecast model.Input vector comprises the characteristic parameter in certain several time period in the past, and the length for input vector should be weighed according to computing velocity and required precision.Generally can be set as according to the next time period inner bearing state of past six hours inner bearing ruuning situation prediction.
After startup forecast model, when there being the new vibration signal gathered to arrive, storage characteristic parameter should be calculated, by new data input values forecast model.
Step 5, carries out the failure prediction of bearing.
Adopt corresponding kernel function forecast model to different parameters, the Changing Pattern of root-mean-square value is comparatively steady, should adopt Matern kernel function; The change of kurtosis index is comparatively violent, should adopt neural network (NN) kernel function.
Application Gaussian process regressive prediction model adopts input vector trains, and iterations is set to 100.Gaussian process regressive prediction model will carry out learning training according to input vector, automatically carry out hyper parameter search by Gaussian process regression algorithm.Iterations generally can be restrained at 80 ~ 120 times.Hyper parameter search algorithm can be sent out by correlation table document, books obtain.
After having trained, Gaussian process regressive prediction model will provide the predicted value of subsequent time vibration signal root-mean-square value and kurtosis index two kinds of characteristic parameters, and carries out trend analysis to two kinds of characteristic parameters, obtains the fiducial interval distribution of failure prediction result and 95%.Keeped in repair timely and change before ensureing bearing fault, parameter prediction should carry out early warning with the marginal value of fiducial interval.Meanwhile, the fault that two kinds of parameter characterizations are dissimilar.Gained predicts the outcome and should carry out predicting that the minimum value of acquired results is as the criterion with two kinds of characteristic parameters.

Claims (1)

1., based on the bearing fault Forecasting Methodology that Gaussian process returns, it is characterized in that: the method concrete steps are as follows:
Step one, setting prognoses system parameter, carries out initialization to Gaussian process regression model;
Setting prognoses system decision threshold 1, decision threshold 2; When the characteristic parameter predicted is higher than decision threshold 1, judge that bearing enters sub-health state, application Gaussian process regression model carries out failure prediction; When the characteristic parameter predicted is higher than decision threshold 2, judge that bearing is by fault, should give maintain and replace;
The setting vibration signals collecting cycle, unsuitable short in the health status down-sampling cycle, after entering sub-health state, reduce the sampling period; For the bearing in continuous firing, under health status, every day samples 1 time, each 1s, and sampling rate is set to 20kHz; Sampling in every 30 minutes 1 time under sub-health state, each 1s, sampling rate is set to 20kHz;
It is a kind of core learning machine algorithm that Gaussian process returns, and should carry out choosing and the setting of hyper parameter initial value of kernel function, hyper parameter initial searching region rule of thumb free setting, hyper parameter initial value is set to zero, is learnt to obtain by Algorithm for Training; The kernel function used in the described bearing fault Forecasting Methodology based on Gaussian process recurrence is square index SE kernel function or neural network NN kernel function;
SE kernel function: C S E ( x , x ′ ) = σ f 2 exp ( - P ( x , x ′ ) 2 2 )
NN kernel function: C N N ( x , x ′ ) = σ f 2 sin - 1 ( 2 x ~ T Σ x ~ ′ ( 1 + 2 x ~ T Σ x ~ ) ( 1 + 2 x ~ ′ Σ x ~ ′ ) )
In formula, symbol description is as follows: order for comprising the vector of all hyper parameter, { P}=l -2i represents hyper parameter I -2with the product matrix of I; for the signal variance of kernel function, the degree of controls local correlativity; for the augmented matrix of x, namely x ~ = ( 1 , x ) T ;
Step 2, taken at regular intervals bearing vibration signal, carries out to vibration signal the time domain charactreristic parameter that feature extraction obtains bearing vibration signal, carries out failure symptom judgement;
Carry out the collection of vibration signal according to the sampling period of setting, and carry out the feature extraction of time domain charactreristic parameter; The most frequently used dimension index that has of process is carried out to bearing vibration signal and comprises root-mean-square value RMS and peak value PEAK, dimensionless index height expands shape factor S, peak factor C, pulse factor I, nargin factor L and kurtosis index K, here using root-mean-square value and kurtosis index as the parameter of failure prediction;
Root-mean-square value RMS can measure the vibratory output of bearing, has both considered the experience process that time of vibration changes, and indicates again the size of mechanical vibrational energy simultaneously; Because root-mean-square value is average to the time, so appropriate evaluation can be had to having surface crack wearing and tearing class fault; The computing formula of root-mean-square value is as follows:
R M S = Σ k = 1 K ( x ( k ) ) 2 K
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used;
Kurtosis index Kurtosis is the tolerance of the high and steep degree of probability density distribution point, represents in vibrational waveform whether have impact or sharp high and steep degree; Kurtosis index is more responsive for shock pulse class failure ratio, especially when fault is early stage, has obvious increase; The computing formula of kurtosis index is as follows:
K u r t o s i s = Σ k = 1 K ( x ( k ) - x m ) 4 Kk s t d 4
In formula, symbol description is as follows: x (k) is burst, wherein k=1, and 2,3 ... K; K is burst data point number used; x mfor signal average, x stdfor signal standards is poor, wherein x mand x stdcomputing formula as follows:
x m = 1 K Σ K = 1 K x ( k )
x s t d = Σ k = 1 K ( x ( k ) - x m ) 2 K - 1
Calculate vibration signal root-mean-square value and kurtosis index respectively, compare with inferior health decision threshold 1, namely think occurred minor failure sign if these two characteristic parameters have one to exceed setting threshold value, bearing enters sub-health state;
Step 3, judges whether the sign that breaks down;
After judgement bearing enters sub-health state, reduce the sampling period of vibration signal, start Gaussian process regression model, carry out failure prediction, proceed to step 4;
When judgement bearing working is normal, when not entering sub-health state, keep current state, return step 2 and continue monitoring vibration signal;
Step 4, the calculating of characteristic parameter and storage, and carry out dynamically updating of Gaussian process regression model;
Calculate vibration signal root-mean-square value and kurtosis index respectively, and these two kinds of characteristic parameters are stored respectively; The characteristic parameter obtained by current time and the characteristic parameter obtained in front several time period, be integrated into Gaussian process regression model input vector, input in this model;
When there being the new vibration signal gathered to arrive, calculating and storing characteristic parameter, and integrating new input vector, upgrade Gaussian process regression model;
Step 5, carries out the failure prediction of bearing;
Application Gaussian process regression model adopts Gaussian process homing method to train to input vector, carries out the root-mean-square value of vibration signal and the trend analysis of kurtosis index two kinds of characteristic parameters, draws failure prediction result and fiducial interval distribution; The fault that two kinds of parameter characterizations are dissimilar, gained predicts the outcome and should carry out predicting that the minimum value of acquired results is as the criterion with two kinds of characteristic parameters.
CN201210323398.3A 2012-09-04 2012-09-04 A kind of bearing fault Forecasting Methodology returned based on Gaussian process CN102831325B (en)

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