CN109241657A - The degeneration modeling of rotating machinery and method for predicting residual useful life under time-varying degradation ratio - Google Patents
The degeneration modeling of rotating machinery and method for predicting residual useful life under time-varying degradation ratio Download PDFInfo
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Abstract
The invention discloses a kind of degeneration modeling of rotating machinery under time-varying degradation ratio and method for predicting residual useful life, step 1, the rotating machinery under time-varying degradation ratio is degenerated modeling；Step 2, the solution of above-mentioned model first-hitting time probability distribution and predicting residual useful life；Step 3, unknown-model parameter Estimation and predicting residual useful life based on detection data are distributed adaptive updates.The present invention is by by rotating machinery time-varying degradation ratio time-varying function λ (t；It θ) describes, the Overlay under initial amount of degradation and time-varying degradation ratio models so as to which rotating machinery is degenerated, can completely show the degraded condition of entire machinery, can be detected in real time by monitoring in real time.
Description
Technical field
The present invention relates to technical field of electronic products, in particular to the degeneration modeling of rotating machinery under a kind of time-varying degradation ratio
And method for predicting residual useful life and electronic product.
Background technique
Remaining life refers to effective time interval of the equipment from current time to failure moment.With the development of science and technology
And progress, the modernization level of modern industry process, manufacturing equipment etc. are continuously improved, the complexity of equipment also constantly increases
Add, it is difficult to establish accurate mechanism model, therefore the method for data-driven be the control for solving this kind of system, it is decision, excellent
Change provides feasible approach.
In the method for data-driven, artificial intelligence approach generally utilizes monitoring data, is set by machine learning with being fitted
The Evolution of standby performance variable, and then pass through the prediction that performance variable of extrapolating realizes remaining life to failure threshold.However,
Such methods often can only obtain the point estimate (i.e. the expectation of remaining life) of predicting residual useful life, it is difficult to portray prediction result
Uncertainty.It is the premise formulated health control strategy, determine optimal maintenance opportunity in view of carrying out predicting residual useful life, and
And in these relevant decisions, the probability distribution of remaining life is generally required, artificial intelligence approach is difficult to obtain embodiment residue
Service life does not know the probability-distribution function of feature at random, therefore such methods have centainly in the relevant decision application of health control
Limitation.In contrast, the method for statistical data driving depends on obtained monitoring data, utilizes statistics or stochastic model pair
Monitoring data are modeled, and then the distribution of remaining life is inferred and predicted, convenient for the uncertain of quantitative prediction result
Property.
Existing degenerate modeling and predicting residual useful life model nearly all assume that the mean degradation rate of equipment is a fixed ginseng
Several or stochastic variable, is unrelated with the time, in practice, the degradation ratio of not all equipment degenerative process is constant, such as tired
The extension of labor crackle during crack propagation at any time can acceleration or deceleration, can change at any time, rotating machinery
Vibration monitoring data are also such.The critical issue that degeneration modeling and predicting residual useful life research under time-varying degradation ratio need to solve
It is: how solves the first-hitting time distribution that random degenerative process when degradation ratio time-varying reaches failure threshold.
Therefore, the degeneration modeling of rotating machinery and method for predicting residual useful life and electronics under a kind of time-varying degradation ratio is invented to produce
Product are necessary to solve the above problems.
Summary of the invention
The purpose of the present invention is to provide a kind of degeneration modeling of rotating machinery under time-varying degradation ratio and predicting residual useful lifes
Method and electronic product, by the Overlay under initial amount of degradation and time-varying degradation ratio, so as to build rotating machinery degeneration
Mould can completely show the degraded condition of entire machinery, can be detected in real time by monitoring in real time, on solving
State the problem of proposing in background technique.
To achieve the above object, the invention provides the following technical scheme: under a kind of time-varying degradation ratio rotating machinery degeneration
Modeling and method for predicting residual useful life, comprising the following steps:
Step 1, the rotating machinery under time-varying degradation ratio are degenerated modeling: by rotating machinery time-varying degradation ratio time-varying function λ
(t；It θ) describes, is based on this, considers that the random process under following time-varying degradation ratio describes the performance degradation process of rotating machinery:
Step 2, the solution of above-mentioned model first-hitting time probability distribution and predicting residual useful life: it is moved back based on established above
Change process, by the concept of first-hitting time, the service life T of equipment be may be defined as:
T=inf t:X (t) >=w | X (0) < w }；
If the corresponding probability density function of first-hitting time T is fT(t), Cumulative Distribution Function FT(t), then have:
WhereinFor time-varying function；
Step 3, unknown-model parameter Estimation and predicting residual useful life based on detection data are distributed adaptive updates: right
In the estimation of model parameter Θ, can will be degenerated by building state of self-organization spatial model by parameter Θ as potential state
Process X (t) is indicated according to Euler discrete strategies, establishes following state of self-organization spatial model:
Wherein original state Θ0~N (a0,P0), η~N (0, Q), Y~N (0,1)；
For state of self-organization spatial model, adaptively estimating for model parameter Θ may be implemented using Bayesian filtering
Meter, can take here Bayesian filtering mainly include EKF filter, Strong tracking filter, particle filter, for
The new parameter a that state of self-organization spatial model introduces0,P0, Q is collectively expressed as parameter vector H, the estimation for H, quasi- to take
The method that Bayesian is smoothly combined with expectation-maximization algorithm estimates H, mainly includes following two step:
Calculate expectation likelihood function:
Maximize expectation likelihood function:
Wherein p () indicates probability density function.
Preferably, in the step 1, wherein B (t) is standard Browian movement, λ (t；θ) and σ is respectively coefficient of deviation
And diffusion coefficient, λ (t；θ) be time t time-varying function, to portray the time-varying degradation ratio feature of degenerative process, θ is model
Unknown parameter vector, initial amount of degradation are X (0)=x0, performance degradation process is in monitoring 0 < t of moment0< t1< K < tkIt obtains
Monitoring data set representations are xi=X (ti), i=0,1, K, k, the time interval of measurement are expressed as Δ ti=ti-ti-1, wherein 1≤i
≤k。
Preferably, in the step 2, the first-hitting time distribution for solving degenerative process { X (t), t >=0 } means that solution
Standard Browian moves to the boundary function dependent on time tFirst-hitting time problem, using standard
Geneva, property of independent increment and the mean-square continuity of Browian movement, by FT(t) solution is further broken into two parts,
A part indicates B (t) on boundaryOn probability, another part be used to describe B (t) t moment fall on boundary but
There is no the probability for reaching boundary to may be implemented by solving this two-part probability to F when moment s < tT(t) solution；It is right
In the remaining life of equipment, in tkMoment can define Sk, it is Sk=inf { sk> tk:X(tk+sk) >=w }, utilize random process { X
(t), t >=0 } geneva, using with solve FT(t) similar method obtains the cumulative distribution function of remaining lifeWherein Θ is all parameters in model, including θ and σ.
Preferably, in the step 3, after the parameter Estimation of degradation model obtains, by estimationIt substitutes intoAdaptive predicting residual useful life can be achieved, if it is considered that available p (Θ after Bayesian filteringk
|Xk), then by total probability formula, update the remaining life distribution of prediction:
Technical effect and advantage of the invention:
1, the present invention is by by rotating machinery time-varying degradation ratio time-varying function λ (t；θ) describe, by initial amount of degradation and when
Become the Overlay under degradation ratio, modeled so as to which rotating machinery is degenerated, can completely show the degeneration of entire machinery
Situation can be detected in real time by monitoring in real time；
2, by first-hitting time to the matter of time of entire probability function, the calculating of remaining life mainly utilizes the present invention
Model parameter Θ may be implemented using Bayesian filtering for state of self-organization spatial model in different realization model parameters
ART network, and by calculate expectation likelihood function and maximize expectation likelihood function come the parameter to entire degradation model
It is calculated.
Detailed description of the invention
Fig. 1 is flowage structure schematic diagram of the invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Embodiment 1:
The present invention provides the degeneration modeling of rotating machinery under a kind of time-varying degradation ratio as shown in Figure 1 and remaining life are pre-
Survey method, including:
Step 1, the rotating machinery under time-varying degradation ratio are degenerated modeling: by rotating machinery time-varying degradation ratio time-varying function λ
(t；It θ) describes, is based on this, considers that the random process under following time-varying degradation ratio describes the performance degradation process of rotating machinery:
Wherein B (t) is standard Browian movement, λ (t；θ) and σ is respectively coefficient of deviation and diffusion coefficient, λ (t；θ) it is
The time-varying function of time t, to portray the time-varying degradation ratio feature of degenerative process, θ is the unknown parameter vector of model, is initially moved back
Change amount is X (0)=x0, performance degradation process is in monitoring 0 < t of moment0< t1< K < tkObtained monitoring data set representations are xi=
X(ti), i=0,1, K, k, the time interval of measurement are expressed as Δ ti=ti-ti-1, wherein 1≤i≤k；
Step 2, the solution of above-mentioned model first-hitting time probability distribution and predicting residual useful life: it is moved back based on established above
Change process, by the concept of first-hitting time, the service life T of equipment be may be defined as: T=inf t:X (t) >=w | X (0) < w }；
If the corresponding probability density function of first-hitting time T is fT(t), Cumulative Distribution Function FT(t), then have:
WhereinFor time-varying function；
The first-hitting time distribution for solving degenerative process { X (t), t >=0 } means that solution standard Browian is moved to
Boundary function dependent on time tFirst-hitting time problem, using standard Browian movement geneva, independence
Incremental and mean-square continuity, by FT(t) solution is further broken into two parts, and a part indicates B (t) on boundaryOn probability, another part is used to describe B (t) and fall on boundary in t moment but do not reach side in moment s < t
The probability on boundary may be implemented by solving this two-part probability to FT(t) solution；For the remaining life of equipment, in tk
Moment can define Sk, it is Sk=inf { sk> tk:X(tk+sk) >=w }, using the geneva of random process { X (t), t >=0 }, adopt
With with solve FT(t) similar method obtains the cumulative distribution function of remaining lifeWherein Θ is
All parameters in model, including θ and σ.
Embodiment 2:
Unlike the first embodiment, the step 3, unknown-model parameter Estimation and remaining life based on detection data
Prediction distribution adaptive updates: the estimation for model parameter Θ, it can be by constructing state of self-organization spatial model, by parameter Θ
As potential state, degenerative process X (t) is indicated according to Euler discrete strategies, establishes following state of self-organization spatial mode
Type:
Wherein original state Θ0~N (a0,P0), η~N (0, Q), Y~N (0,1)；
For state of self-organization spatial model, adaptively estimating for model parameter Θ may be implemented using Bayesian filtering
Meter, can take here Bayesian filtering mainly include EKF filter, Strong tracking filter, particle filter, for
The new parameter a that state of self-organization spatial model introduces0,P0, Q is collectively expressed as parameter vector H, the estimation for H, quasi- to take
The method that Bayesian is smoothly combined with expectation-maximization algorithm estimates H, mainly includes following two step:
Calculate expectation likelihood function:
Maximize expectation likelihood function:
Wherein p () indicates probability density function；
After the parameter Estimation of degradation model obtains, by estimationIt substitutes intoIt can be achieved adaptive
Predicting residual useful life, if it is considered that Bayesian filtering after available p (Θk|Xk), then by total probability formula, update pre-
The remaining life of survey is distributed:
Finally, it should be noted that the foregoing is only a preferred embodiment of the present invention, it is not intended to restrict the invention,
Although the present invention is described in detail referring to the foregoing embodiments, for those skilled in the art, still may be used
To modify the technical solutions described in the foregoing embodiments or equivalent replacement of some of the technical features,
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (4)
1. the degeneration modeling of rotating machinery and method for predicting residual useful life under a kind of time-varying degradation ratio, which is characterized in that including with
Lower step:
Step 1, the rotating machinery under time-varying degradation ratio are degenerated modeling: by rotating machinery time-varying degradation ratio time-varying function λ (t；
It θ) describes, is based on this, considers that the random process under following time-varying degradation ratio describes the performance degradation process of rotating machinery:
Step 2, the solution of above-mentioned model first-hitting time probability distribution and predicting residual useful life: based on degeneration established above
Journey, by the concept of first-hitting time, the service life T of equipment be may be defined as:
T=inf t:X (t) >=w | X (0) < w }；
If the corresponding probability density function of first-hitting time T is fT(t), Cumulative Distribution Function FT(t), then have:
WhereinFor time-varying function；
Step 3, unknown-model parameter Estimation and predicting residual useful life based on detection data are distributed adaptive updates: for mould
The estimation of shape parameter Θ, can be by constructing state of self-organization spatial model, by parameter Θ as potential state, by degenerative process
X (t) is indicated according to Euler discrete strategies, establishes following state of self-organization spatial model:
Wherein original state Θ0~N (a0,P0), η~N (0, Q), Y~N (0,1)；
For state of self-organization spatial model, the ART network of model parameter Θ may be implemented using Bayesian filtering, this
In can take Bayesian filtering mainly include EKF filter, Strong tracking filter, particle filter, for self-organizing
The new parameter a that state-space model introduces0,P0, Q is collectively expressed as parameter vector H, the estimation for H, quasi- to take Bayesian
The method smoothly combined with expectation-maximization algorithm estimates H, mainly includes following two step:
Calculate expectation likelihood function:
Maximize expectation likelihood function:
Wherein p () indicates probability density function.
2. the degeneration modeling of rotating machinery and predicting residual useful life side under a kind of time-varying degradation ratio according to claim 1
Method, it is characterised in that: in the step 1, wherein B (t) is standard Browian movement, λ (t；θ) and σ is respectively coefficient of deviation
And diffusion coefficient, λ (t；θ) be time t time-varying function, to portray the time-varying degradation ratio feature of degenerative process, θ is model
Unknown parameter vector, initial amount of degradation are X (0)=x0, performance degradation process is in monitoring 0 < t of moment0< t1< K < tkIt obtains
Monitoring data set representations are xi=X (ti), i=0,1, K, k, the time interval of measurement are expressed as Δ ti=ti-ti-1, wherein 1≤i
≤k。
3. the degeneration modeling of rotating machinery and predicting residual useful life side under a kind of time-varying degradation ratio according to claim 1
Method, it is characterised in that: in the step 2, the first-hitting time distribution for solving degenerative process { X (t), t >=0 } means that solution
Standard Browian moves to the boundary function dependent on time tFirst-hitting time problem, using standard
Geneva, property of independent increment and the mean-square continuity of Browian movement, by FT(t) solution is further broken into two parts,
A part indicates B (t) on boundaryOn probability, another part be used to describe B (t) t moment fall on boundary but
There is no the probability for reaching boundary to may be implemented by solving this two-part probability to F when moment s < tT(t) solution；It is right
In the remaining life of equipment, in tkMoment can define Sk, it is Sk=inf { sk> tk:X(tk+sk) >=w }, utilize random process { X
(t), t >=0 } geneva, using with solve FT(t) similar method obtains the cumulative distribution function of remaining lifeWherein Θ is all parameters in model, including θ and σ.
4. the degeneration modeling of rotating machinery and predicting residual useful life side under a kind of time-varying degradation ratio according to claim 1
Method, it is characterised in that: in the step 3, after the parameter Estimation of degradation model obtains, by estimationIt substitutes intoAdaptive predicting residual useful life can be achieved, if it is considered that available p (Θ after Bayesian filteringk
|Xk), then by total probability formula, update the remaining life distribution of prediction:
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111160666A (en) * | 2020-01-02 | 2020-05-15 | 西北工业大学 | Health state and reliability assessment method for monitoring strong noise and non-periodic state |
| CN112800616A (en) * | 2021-02-05 | 2021-05-14 | 中国人民解放军空军工程大学 | Equipment residual life self-adaptive prediction method based on proportional acceleration degradation modeling |
| CN112949204A (en) * | 2021-03-22 | 2021-06-11 | 西安交通大学 | Rolling bearing residual life prediction method with data and model adaptive matching |
-
2018
- 2018-09-27 CN CN201811130618.4A patent/CN109241657A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111160666A (en) * | 2020-01-02 | 2020-05-15 | 西北工业大学 | Health state and reliability assessment method for monitoring strong noise and non-periodic state |
| CN112800616A (en) * | 2021-02-05 | 2021-05-14 | 中国人民解放军空军工程大学 | Equipment residual life self-adaptive prediction method based on proportional acceleration degradation modeling |
| CN112949204A (en) * | 2021-03-22 | 2021-06-11 | 西安交通大学 | Rolling bearing residual life prediction method with data and model adaptive matching |
| CN112949204B (en) * | 2021-03-22 | 2022-12-09 | 西安交通大学 | Rolling bearing residual life prediction method with data and model adaptive matching |
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