CN108829983A - Equipment method for predicting residual useful life based on more hidden state fractional Brownian motions - Google Patents
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Abstract
The present invention relates to electromechanical equipment life prediction fields, disclose a kind of equipment method for predicting residual useful life based on more hidden state fractional Brownian motions, it solves to only take into account current observation, the low problem of equipment life precision of prediction in traditional equipment method for predicting residual useful life based on fractional Brownian motion.Nonlinear function is chosen according to the life deterioration trend of equipment first, non-linear Fractional Brownian Motion Model is determined, by the parameter in nonlinear function as hidden state；Non-linear Fractional Brownian Motion Model is converted into non-linear Brownian Motion Model again；It carries out curve fitting again to training data, obtains the initial value of hidden state mean value；Iteration updates the mean value and variance of hidden state again, obtains the distribution function of hidden state；The posterior probability Density Distribution of attack time first time is derived again；Finally life prediction is carried out with the posterior probability Density Distribution of attack time first time.The remaining useful life that the present invention is suitable for electromechanical equipment is predicted.
Description
Technical field
The present invention relates to electromechanical equipment life prediction fields, more particularly to setting based on more hidden state fractional Brownian motions
Standby method for predicting residual useful life.
Background technique
With the rapid development of modern science and technology industrial technology and the continuous improvement of functional requirement, a large amount of electromechanical equipments are gradually in
Reveal complication, synthesization and intelligentized trend, the health control ability of these trend urgent need electromechanical equipment and can
By the promotion of property.Electromechanical equipment has inevitable performance degradation in the process of running.When the performance degradation of equipment is to equipment
When being not enough to complete its function, equipment downtime even failure will lead to, bring huge economic loss even casualties.Accurately
The remaining useful life of pre- measurement equipment be capable of providing correct effective maintenance policy, thus in the thing for avoiding these serious safeties
Therefore it plays an important role with economic loss aspect.Therefore, the system failure is had become for the prediction of equipment remaining useful life
The research hotspot of prediction and health management arts.Can power supply of the lithium battery as many electromechanical equipments provide equipment institute
Power is needed to have significant impact for the safe operation of electromechanical equipment.Therefore, also very must to the predicting residual useful life of lithium battery
It wants.
Two classes are broadly divided into for the method for the remaining useful life prediction of equipment at present：One kind is based on regression model
Method, such methods rely primarily on the state-space model being made of state equation and measurement equation and regression analysis, such as
In conjunction with the method for the experience degenrate function and particle filter that are obtained by lithium battery degraded data；Second class is based on random process
The method of model, such methods are mainly by equipment degenerative process as random process, then by random process, such as gamma mistake
Journey, markoff process, Wiener-Hopf equation etc. to characterize degenerative process, and then analytically obtain the posteriority of attack time first time
Distribution function.Since the probability-distribution function of attack time first time is dead wind area, linear Brownian Motion Model is in residue
Useful life prediction has received widespread attention in field.However engineering is in practice, most of equipment degenerative process shows non-
Linear characteristic causes linear Brownian Motion Model to use limited.Attack time first time of subsequent non-linear Brownian Motion Model
Distribution function obtained by space-time conversion approximation, this is widely used non-linear Brownian Motion Model.But
It is that Brownian Motion Model assumes that increment is independent in entire degenerative process, this is not inconsistent with some equipment degenerative processes,
Such as lithium battery, bearing etc..There are correlations for increment in these equipment degenerative processes, that is to say, that these degenerative processes exist it is long according to
Lai Xing.Non-linear Fractional Brownian Motion Model is introduced for carrying out these degenerative processes that there are the residues of the equipment of long dependence to have
It imitates life prediction, the problem of effective solution related increment, but is based on non-linear fractional Brownian motion mould in document before
Model Parameter as constant, can be existed only take into account asking for current observation in this way by the method for predicting residual useful life of type
Topic.
Summary of the invention
The technical problem to be solved by the present invention is to：It is remaining to provide a kind of equipment based on more hidden state fractional Brownian motions
Life-span prediction method solves to only take into account current sight in traditional equipment method for predicting residual useful life based on fractional Brownian motion
Measured value, the low problem of equipment life precision of prediction.
To solve the above problems, the technical solution adopted by the present invention is that：Based on setting for more hidden state fractional Brownian motions
Standby method for predicting residual useful life, includes the following steps：
Step 1：Nonlinear function is chosen according to the life deterioration trend of equipment, and determines non-linear point of nonlinear function
Number Brownian Motion Model, and by the parameter in nonlinear function as unobservable state variable, unobservable state becomes
Amount is hidden state；
Step 2：Non-linear Fractional Brownian Motion Model is converted into non-linear Brownian Motion Model；
Step 3：Training data is chosen, and is carried out curve fitting based on the nonlinear function that step 1 is chosen to training data,
The initial value of hidden state mean value is obtained by matched curve；
Step 4：The mean value and variance that hidden state is updated using the history degraded data iteration of equipment, obtain hidden state
Distribution function；
Step 5：In conjunction with the distribution function of hidden state, the posterior probability Density Distribution of attack time first time is derived；
Step 6：The remaining useful life of equipment is predicted with the posterior probability Density Distribution of attack time first time.
Further, the non-linear Fractional Brownian Motion Model that step 1 determines is as follows：
Wherein, X (t) is the state of equipment t moment；X (0) is original state；μ(τ；It θ) is nonlinear function；τ is non-thread
Property function in integration variable, θ be nonlinear function in parameter vector；σHFor coefficient of deviation；BHIt (t) be Hurst Exponent is H
Fractional Brownian motion function.
Further, it preferably carries out curve fitting to training data in order to which step 3 allows, the non-linear letter that step 1 is chosen
Number is：
μ(τ；θ)=abexp (b τ)+cdexp (d τ)
Wherein, a, b, c and d are the parameter in nonlinear function, θ=[a, b, c, d].
Further, non-linear Fractional Brownian Motion Model is converted to non-linear Blang by Theory of Weak Convergence by step 2
Motion model.
Further, step 3 chooses the Battery Data that NASA's brilliance failure predication center provides
Set test data is as training data.
Further, for mean value and variance that better iteration updates hidden state, step 4 uses tasteless particle filter
Method iteration update hidden state mean value and variance.
Further, step 4 obtains the distribution function of hidden state and is：
Wherein, mkIndicate the mean value of the hidden state at k moment, PkIndicate the variance of the hidden state at k moment, X0:kIndicate 0
To the particle observation at k moment, θkIndicate the unobservable state variable at k moment.
Further, the posterior probability density fonction of attack time first time of step 5 derivation is：
Wherein：lkFor remaining useful life, ωthFor capacitance threshold value,
NsFor number of particles,Weight for i-th of particle at the k moment,Value for i-th of particle in k moment hidden state, σ
(t) time-varying coefficient to be generated when Fractional Brownian Motion Model is converted to Brownian Motion Model.
The beneficial effects of the invention are as follows：The present invention is by by the ginseng of nonlinear function in non-linear Fractional Brownian Motion Model
Number comes as hidden variable so that model is more flexible, and using the method for tasteless particle filter, historical data is used for iteration
The mean value and variance for updating multiple hidden states, obtain the distribution function of hidden state；Meanwhile the present invention by double-exponential function it
With as the nonlinear function in non-linear Fractional Brownian Motion Model, approximation obtains the Posterior distrbutionp letter of attack time first time
Number finally realizes the remaining useful life prediction to lithium battery, improves the life prediction precision of equipment.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 a- Fig. 2 c be at 40,45,50,55,60,65,70Cycle, method 4 respectively with method 1-3 prediction result
Comparison diagram；
Fig. 3 is the relative error comparison diagram of four kinds of method prediction results at 40,45,50,55,60,65,70Cycle.
In figure：L1-L4 respectively indicates the probability density function curve for the remaining useful life that method 1 to method 4 is predicted；
A indicates true remaining lifetime value；M1-M4 distinguish method 1 to method 4 prediction result relative error curve.
Specific embodiment
Equipment method for predicting residual useful life based on more hidden state fractional Brownian motions of the invention, as shown in Figure 1, packet
Include following steps：
Step 1：Nonlinear function is chosen according to the life deterioration trend of equipment, and determines non-linear point of nonlinear function
Number Brownian Motion Model, and by the parameter in nonlinear function as unobservable state variable, unobservable state becomes
Amount is hidden state.The step can choose μ (τ；θ)=abexp (b τ)+cdexp (d τ) is used as nonlinear function,
Wherein, a, b, c and d are the parameter in nonlinear function, θ=[a, b, c, d]；And then non-linear score cloth determined by step 1
Bright motion model is：Wherein, X (t) is the state of equipment t moment；X (0) is
Original state generally takes 0；μ(τ；It θ) is nonlinear function；τ is the integration variable in nonlinear function, and θ is in nonlinear function
Parameter vector；σHFor coefficient of deviation；BHIt (t) is fractional Brownian motion.
Step 2：Non-linear Fractional Brownian Motion Model is converted into non-linear Brownian Motion Model.The step can pass through
Non-linear Fractional Brownian Motion Model is converted to non-linear Brownian Motion Model by Theory of Weak Convergence.
Step 3：Training data is chosen, and is carried out curve fitting based on the nonlinear function that step 1 is chosen to training data,
The initial value of hidden state mean value is obtained by matched curve.The step can choose NASA's brilliance failure predication
The Battery Data Set test data that center provides is as training data.
Step 4：The mean value and variance that hidden state is updated using the history degraded data iteration of equipment, obtain hidden state
Distribution function.The step can update the mean value and variance of hidden state using the method iteration of tasteless particle filter.
Step 5：In conjunction with the distribution function of hidden state, the posterior probability Density Distribution of attack time first time is derived.
Step 6：It is carried out in advance with remaining useful life of the posterior probability Density Distribution of attack time first time to lithium battery
It surveys.
The present invention by by the parameter of nonlinear function in non-linear Fractional Brownian Motion Model as hidden variable, to make
Model it is more flexible, and using tasteless particle filter method, historical data is used for iteration and updates multiple hidden states
Mean value and variance obtain the distribution function of hidden state；Meanwhile the present invention regard the sum of double-exponential function as non-linear score cloth
Nonlinear function in bright motion model, approximation obtain the Posterior distrbutionp function of attack time first time, finally realize to lithium electricity
The remaining useful life in pond is predicted.
Embodiment
It is remaining to provide a kind of equipment based on more hidden state fractional Brownian motions by taking lithium ion battery as an example for embodiment
Life-span prediction method, specific step is as follows：
Step 1：Nonlinear function is chosen according to the life deterioration trend of equipment, and determines non-linear point of nonlinear function
Number Brownian Motion Model, and by the parameter in nonlinear function as unobservable state variable, unobservable state becomes
Amount is hidden state.
The step is using the experience degenrate function of lithium battery as the nonlinear function in non-linear Fractional Brownian Motion Model.
The nonlinear function of selection is：
μ(τ；θ)=abexp (b τ)+cdexp (d τ)
Wherein, τ is the variable in nonlinear function, and a, b, c and d are the parameter in nonlinear function；
Above-mentioned non-linear Fractional Brownian Motion Model is：
X (t)=X (0)+aexp (bt)+cexp (dt)+σHBH(t)
X (t) is function of state, is lithium battery capacity in the example；X (0) is initial value, is set as 0 here；BHIt (t) is conspicuous
This refers in particular to the fractional Brownian motion that number is H；σHFor coefficient of deviation.
In this embodiment, hidden state is set by θ=[a, b, c, d].
Step 2：Non-linear Fractional Brownian Motion Model is converted into non-linear Brownian Motion Model by Theory of Weak Convergence.
Because above-mentioned degenerative process is neither markoff process is also not semimartingale process, for the first Secondary Shocks
Time, cutting cloth was difficult to derive really, and embodiment can use Theory of Weak Convergence, and non-linear Fractional Brownian Motion Model is close
Non-linear Brownian Motion Model is seemingly converted to, approximate non-linear Brownian Motion Model can be expressed as：
B (t) is standard Brownian movement；σ (t) is time-varying coefficient, can be expressed as：
cHFor generalized constant, it is represented by：
Step 3：Training data is chosen, and is carried out curve fitting based on nonlinear function to training data, it is bent by fitting
Line obtains the initial value of hidden state mean value.
The step utilizes given nonlinear function, and NASA's brilliance failure predication center is provided
Battery Data Set test data is as training data, and this example is using B0006, B0007 and B0018 battery data as training
Data, B0005 battery data is used to do life prediction, using matlab Curve Fitting Toolbox to B0006, B0007 and B0018
Battery data carries out curve fitting.
Then the parameter value of matched curve obtained above is averaged to the initial value that hidden state mean value can be obtained.
Step 4：Using the method for tasteless particle filter, the mean value of iteration update hidden state is gone using history degraded data
And variance, obtain the distribution function of hidden state.
It will no longer be a constant, in this example when θ=[a, b, c, d] is taken as hidden state, it is assumed that θ obeys one 4
Tie up the multivariate Gaussian distribution of mean vector m and one 4 × 4 dimension variance matrix P.State-space model can be described as：
θk=θk-1+ν
xk=xk-1+φ(k)-φ(k-1)+σ(tk)B(tk)-σ(tk-1)B(tk-1)+n
Wherein：
φ (k)=ak·exp(bktk)+ck·exp(dktk)
ν is state error, obeys the multivariate Gaussian point of one 40 mean vector of dimension and one 4 × 4 dimension variance matrix Q
Cloth；N is error in measurement, obeys a zero mean vector and the multivariate Gaussian distribution of a variance matrix R；Utilize history number
According to, above-mentioned state-space model is solved, it can the posterior mean value and variance for estimating hidden state.Tasteless particle filter is existing
There is technology, the tasteless particle filter of embodiment estimates that the process of hidden state mean value and variance is as follows：
(1) it initializes；
(2) it is generated using Unscented Kalman Filter and suggests distribution；
It is above-mentioned,For the particle of selection；λ is the parameter of tasteless transformation；WithRespectively first-order statistics characteristic and
The weight coefficient of second-order statistics；mk|k-1、Pk|k-1And Zk|k-1It is quantity of state, the one-step prediction of variance and measuring value respectively；KkFor
Filtering gain；WithRespectively the Unscented Kalman Filter last mean value arrived and variance；ωkFor particle weights.
(3) importance sampling and weight calculation；
N is taken from suggestion obtained above distributionsA particle, wherein particle is obeyed
It is as follows to calculate weight equation：
(4) resampling；
If effective number of particles is lower than threshold value, resampling is carried out, readopts N from current particle concentrationsA grain
Son.Threshold calculations formula is as follows：
(5) it exports；
Hidden state mean value computation formula is as follows:
If k is less than or equal to newest observation time T, k=k+1 is enabled, and return to (2) step, otherwise output prediction knot
Fruit.
After obtaining mean value and variance, the distribution function of hidden state is can be obtained in the normal distyribution function for bringing standard into,
The distribution function of hidden state is represented by：
In formula, mkIndicate the mean value of the hidden state at k moment, PkIndicate the variance of the hidden state at k moment, X0:kIt indicates
0 arrives the particle observation at k moment, θkIndicate the unobservable state variable at k moment.
Step 5：In conjunction with the distribution function of hidden state, the posterior probability Density Distribution of attack time first time is derived.
Under the non-linear Fractional Brownian Motion Model of more hidden states, the posterior probability Density Distribution of attack time first time
Function can be represented as：
With step 4 particle generated and weight come approximate above-mentioned integral calculation, available following result：
Wherein：
lkFor remaining useful life, ωthFor capacitance threshold value, i.e. battery capacity is lower than ωthIt is considered as failing, NsFor grain
Subnumber mesh,Weight for i-th of particle at the k moment,It is i-th of particle in the value of k moment hidden state, σ (t) is will
Fractional Brownian Motion Model is converted to the time-varying coefficient generated when Brownian Motion Model.
Step 6：It is carried out in advance with remaining useful life of the posterior probability Density Distribution of attack time first time to lithium battery
It surveys.
Given Life threshold value calculates the Posterior distrbutionp of attack time first time by the formula that step 6 obtains.?
It is as shown in Figure 3 to B0005 battery progress remaining useful life prediction result using mentioned method when 70Cycle, it can be seen that
In 70Cycle, prediction model can be very good the degradation trend of tracking capacity, and predict obtained attack time first time
The peak value of Posterior distrbutionp function and true remaining life very close to, it is possible thereby to illustrate the mentioned method of the present invention to lithium battery into
Row remaining useful life can obtain good precision when predicting.
In order to verify the superiority for the method that embodiment is proposed, the mentioned method of embodiment and other three kinds of methods are carried out pair
Than four kinds of methods are described as follows：
Method 1：Using the non-linear Fractional Brownian Motion Model for being free of hidden state, wherein nonlinear function μ (τ；θ) select
With nonlinear function abexp (b the τ)+cdexp (d τ) mentioned, iteration update method is tasteless particle filter；
Method 2：Using the non-linear Fractional Brownian Motion Model of more hidden states, wherein nonlinear function μ (τ；θ) select
Nonlinear function abexp (b the τ)+cdexp (d τ) mentioned, iteration update method are particle filter；
Method 3：Using the non-linear Fractional Brownian Motion Model of more hidden states, wherein nonlinear function μ (τ；θ) select
The present common nonlinear function abexp of document (b τ), iteration update method are tasteless particle filter；
Method 4：Using the non-linear Fractional Brownian Motion Model of more hidden states, wherein nonlinear function μ (τ；θ) select
Nonlinear function abexp (b the τ)+cdexp (d τ) mentioned, iteration update method are tasteless particle filter, that is, are implemented
The mentioned method of example；
Also, in order to verify the robustness of proposed method, embodiment is in lithium battery 40,45,50,55,60,65,70Cycle
Etc. different time points carried out remaining useful life prediction respectively.In different predicted times, method 4 is predicted with method 1-3 respectively
As a result the prediction result of comparison diagram is compared as shown in Fig. 2 a- Fig. 2 c.Fig. 3 gives four kinds of methods and misses in the prediction of different time
Difference.As seen in Figure 3, embodiment is in non-linear fractional Brownian motion using the parameter of nonlinear function as hidden state
A promotion on model；The mean value for updating hidden state and variance is gone also to compare grain for available one using tasteless particle filter
Son filters better result；Compared to the nonlinear function in existing literature, mentioned nonlinear function can also be tracked preferably
The degradation trend of lithium battery.Generally speaking, embodiment can significantly improve precision of prediction.
Claims (8)
1. the equipment method for predicting residual useful life based on more hidden state fractional Brownian motions, which is characterized in that including following step
Suddenly：
Step 1：Nonlinear function is chosen according to the life deterioration trend of equipment, and determines the non-linear score cloth of nonlinear function
Bright motion model, and by the parameter in nonlinear function as unobservable state variable, unobservable state variable is
Hidden state；
Step 2：Non-linear Fractional Brownian Motion Model is converted into non-linear Brownian Motion Model；
Step 3：Training data is chosen, and is carried out curve fitting based on the nonlinear function that step 1 is chosen to training data, is passed through
Matched curve obtains the initial value of hidden state mean value；
Step 4：The mean value and variance that hidden state is updated using the history degraded data iteration of equipment obtain point of hidden state
Cloth function；
Step 5：In conjunction with the distribution function of hidden state, the posterior probability Density Distribution of attack time first time is derived；
Step 6：The remaining useful life of equipment is predicted with the posterior probability Density Distribution of attack time first time.
2. the equipment method for predicting residual useful life as described in claim 1 based on more hidden state fractional Brownian motions, special
Sign is that the non-linear Fractional Brownian Motion Model that step 1 determines is as follows：
Wherein, X (t) is the state of equipment t moment；X (0) is original state；μ(τ；It θ) is nonlinear function；τ is non-linear letter
Integration variable in number, θ are the parameter vector in nonlinear function；σHFor coefficient of deviation；BH(t) be Hurst Exponent be H point
Number Brownian movement function.
3. the equipment method for predicting residual useful life as claimed in claim 2 based on more hidden state fractional Brownian motions, special
Sign is that the nonlinear function that step 1 is chosen is：
μ(τ；θ)=abexp (b τ)+cdexp (d τ)
Wherein, a, b, c and d are the parameter in nonlinear function, θ=[a, b, c, d].
4. the equipment method for predicting residual useful life as described in claim 1 based on more hidden state fractional Brownian motions, special
Sign is that non-linear Fractional Brownian Motion Model is converted to non-linear Brownian Motion Model by Theory of Weak Convergence by step 2.
5. the equipment method for predicting residual useful life as described in claim 1 based on more hidden state fractional Brownian motions, special
Sign is that step 3 chooses the Battery Data Set test data that NASA's brilliance failure predication center provides
As training data.
6. the equipment method for predicting residual useful life as described in claim 1 based on more hidden state fractional Brownian motions, special
Sign is that step 4 updates the mean value and variance of hidden state using the method iteration of tasteless particle filter.
7. the equipment method for predicting residual useful life as described in claim 1 based on more hidden state fractional Brownian motions, special
Sign is that the distribution function that step 4 obtains hidden state is：
Wherein, mkIndicate the mean value of the hidden state at k moment, PkIndicate the variance of the hidden state at k moment, X0:kWhen indicating 0 to k
The particle observation at quarter, θkIndicate the unobservable state variable at k moment.
8. the equipment method for predicting residual useful life as claimed in claim 7 based on more hidden state fractional Brownian motions, special
Sign is that the posterior probability density fonction for attack time first time that step 5 derives is：
Wherein：lkFor remaining useful life, ωthFor capacitance threshold value, NsFor
Number of particles,Weight for i-th of particle at the k moment,It is i-th of particle in the value of k moment hidden state, σ (t) is
The time-varying coefficient generated when Fractional Brownian Motion Model is converted to Brownian Motion Model.
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