CN109101778B - Parameter estimation method of Wiener process based on fusion of performance degradation data and life data - Google Patents
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Abstract
本发明属于可靠性统计技术领域，本发明公开了基于性能退化数据和寿命数据融合的Wiener过程参数估计方法，先利用性能退化数据，根据极大似然法求得Wiener过程参数的初值，再利用该初值估计寿命数据的失效概率，最后拟合失效概率和寿命数据估计寿命分布参数，并转化为Wiener过程参数的最终值。本发明通过上述步骤很好的解决了基于性能退化数据和寿命数据融合的Wiener过程参数估计问题。相比现有方法，本发明所提出的算法计算过程简单有效。通过下述具体实施方式可知，本发明所提出的算法计算精度很高。
The invention belongs to the technical field of reliability statistics, and discloses a Wiener process parameter estimation method based on the fusion of performance degradation data and life data. Use the initial value to estimate the failure probability of the life data, and finally fit the failure probability and life data to estimate the life distribution parameters, and convert them into the final values of the Wiener process parameters. The present invention solves the problem of Wiener process parameter estimation based on the fusion of performance degradation data and life data well through the above steps. Compared with the existing method, the calculation process of the algorithm proposed by the present invention is simple and effective. It can be seen from the following specific embodiments that the algorithm proposed by the present invention has high calculation accuracy.
Description
Technical field
Present invention relates generally to reliability statistics fields, refer in particular to a kind of based on Performance Degradation Data and lifetime data fusion
Wiener procedure parameter estimation method.
Background technique
In Reliability Engineering, the reliability estimation method based on lifetime data is traditional technology.This method is main
It is to be distributed using mathematical statistics using the specific service life, assesses the reliable of product by analyzing the lifetime data of product
Property.But with the progress of science and technology, the reliability of the raising of manufacturing process, product is higher and higher, has been difficult to be collected into a large amount of
Lifetime data, cause traditional reliability estimation method based on lifetime data to be difficult to be applicable in.
For this purpose, the reliability estimation method based on Performance Degradation Data has obtained broad development.This method is mainly logical
The excessively degenerative process of analysis properties of product data degenerates to the time of specific threshold by analysis properties of product to assess product
Reliability.
Wiener process is widely used in the reliability estimation method based on Performance Degradation Data.Remember the performance number of product
According to forIf it meets following property:
(1) momentTo the momentBetween increment Normal Distribution, i.e.,；
(2) to the disjoint time interval of any two,,, incrementWithIndependently of each other；
(3)And?Continuously.
ThenUnitary Wiener process is obeyed, and claims parameterFor drift parameter,It is diffusion parameter [with reference to text
It offers: Reliability Modeling research National University of Defense technology doctoral thesis of the Peng Baohua based on Wiener process, 2010.].
If the degradation of product is, i.e., when the performance of product degenerates to for the first timeWhen, product will fail, and at this time may be used
Push away to obtain life of productBe distributed as dead wind area, and life of productDistribution function be
(1)
WhereinIt is standardized normal distribution,,。
If existing simultaneously Performance Degradation Data and lifetime data, can carry out based on Performance Degradation Data and lifetime data
The Reliability Assessment method of fusion, key among these are Wiener procedure parametersWithEstimation.For both
The fusion of data, current is mostly that Wiener procedure parameter is estimated by Bayes theory, such as by Performance Degradation Data and service life number
Get up tectonic syntaxis likelihood function according to fusion, or converts prior distribation for Performance Degradation Data and merged with lifetime data, or general
Lifetime data is converted into prior distribation and merges with Performance Degradation Data.But these method for parameter estimation are directed to complicated number
Student movement is calculated, and engineering practice is not easy to.
Summary of the invention
The technical problem to be solved in the present invention is that: when the one-parameter Performance Degradation Data and service life for being collected simultaneously product
When data, and the Performance Degradation Data obedience parameter of product isWithUnitary Wiener process, the service life number of product at this time
According to the dead wind area obeyed in formula (1).It now needs to assess product by the Performance Degradation Data and lifetime data of fusion product
Reliability, key therein are how to estimate drift parameterAnd diffusion parameter.In order to solve the above-mentioned technical problem, of the invention
It is proposed the Wiener procedure parameter estimation method merged based on Performance Degradation Data and lifetime data.This method can simplify entirely
Mathematical operation in calculating process, and can guarantee the precision of calculated result.
The technical scheme is that
The Wiener procedure parameter estimation method merged based on Performance Degradation Data and lifetime data, comprising the following steps:
(1) utility degraded data estimates drift parameter according to maximum-likelihood methodAnd diffusion parameterInitial value:
If sharedA sample carries out performance degradation experiment to collect Performance Degradation Data.To sample, initial time
Performance measurement is, exist respectivelyMoment measures samplePerformance obtain its performance measurement and be respectively。
NoteIt is sampleAt the momentWithBetween performance degradation amount, according to
Known to the property of Wiener process
Wherein,,。
Then according to Maximum Likelihood Estimation Method, Performance Degradation DataLikelihood function be
Parameter can be acquired by likelihood functionWithMaximum-likelihood estimation be
(2)
It acquiresWithAs parameterWithInitial value.
(2) failure probability of life expectancy data.
If the degradation of product is, i.e., when the performance of product degenerates to for the first timeWhen, product will fail.In the service life
The performance measurement of each sample product is measured in test, cannot be worked on if a certain moment starts a certain sample product and is worked as production
The performance measurement of product degenerates to for the first timeWhen, then the moment is lifetime data namely its out-of-service time of the sample product.
If shared(M and the n in step (1) are not related, i.e., M is likely larger than n, it is also possible to be less than n, it is also possible to be equal to
N, should be subject to the data volume being actually collected into) a sample products carry out life test to collect lifetime data；If being collected into
A lifetime data isIt the out-of-service time of a sample products, is denoted as, and set；Then utilize step
(1) solution obtains inWith, life expectancy data as the following formulaFailure probability:
Wherein,,。
(3) the failure probability estimation procedure parameter of lifetime data is utilized.
According to all pointsIt is fitted product life distribution curve, wherein, that is, it is based on curve matching
Thought, utilize trusted zones reflect (trust region reflective) algorithm, solving optimization model
Obtain inverse Gauss service life distribution parameterWithEstimation, be denoted asWith, then Wiener procedure parameter can be obtained
WithBe estimated as
(3)
As described above, the present invention is asked first with Performance Degradation Data according to maximum-likelihood method according to step shown in FIG. 1
Wiener procedure parameter initial value, recycle the failure probability of the initial estimate lifetime data, finally be fitted failure probability and
Lifetime data life expectancy distribution parameter, and it is converted into the end value of Wiener procedure parameter.The present invention is through the above steps very
The good Wiener procedure parameter estimation problem solved based on Performance Degradation Data and lifetime data fusion, compares existing side
Method, algorithm calculating process proposed by the invention are simple and effective.By following specific embodiments it is found that proposed by the invention
Algorithm computational accuracy is very high.
Detailed description of the invention
Fig. 1 is flow chart of the invention,
Fig. 2 is the performance measurement of present example.
Specific embodiment
The present invention is described in further details below with reference to example and attached drawing.
This example discloses a kind of Wiener procedure parameter estimation side merged based on Performance Degradation Data and lifetime data
Method.In this example, it is assumed that have 6 samples, and the performance degradation amount of each sample obeys parameterWith's
Wiener process.6 groups of random numbers are generated based on the Wiener process, each group respectively there are 10001 numerical value, as 6 samples
Performance measurement, as shown in Figure 2.In addition, generating 6 random numbers based on dead wind area corresponding to the Wiener process and making
It is 1.4257,1.5118,1.5365,1.5641,2.2672 and 2.4917 for the lifetime data of 6 samples.Of the invention
Specific algorithm is as follows:
Firstly, based on the performance measurement in Fig. 2, acquiring Wiener procedure parameter using formula (2) according to maximum-likelihood method
Initial value beWith。
Then the service life distribution parameter initial value converted according to Wiener procedure parameter initial value, estimates 6 lifetime datas
Failure probability can obtain 0.2106,0.2631,0.2787,0.2962,0.7029 and 0.7895.
It is finally fitted 6 groups of lifetime datas and failure probability point estimation, inverse Gauss service life distribution parameter is acquired, is then converted to
The end value of Wiener procedure parameter can obtainWith。
By above example it is found that utilizing the Wiener for merging Performance Degradation Data and lifetime data proposed by the invention
Procedure parameter estimation method, the Wiener procedure parameter estimated value and true value acquired is very close, this demonstrate that the present invention is mentioned
The accuracy of method out.
Claims (1)
1. the Wiener procedure parameter estimation method merged based on Performance Degradation Data and lifetime data, it is characterised in that: including
Following steps:
(1) utility degraded data estimates the initial value of drift parameter μ and diffusion parameter σ according to maximum-likelihood method；
If shared n sample products carry out performance degradation experiment to collect Performance Degradation Data；For sample products i, when initial
Carve ti0Performance measurement is Xi0=0, exist respectivelyThe performance of moment measurement sample products i obtains its performance measurement point
It is not
Remember Δ xij=Xij-Xi(j-1)It is sample products i in moment ti(j-1)And tijBetween performance degradation amount, according to Wiener mistake
Known to the property of journey
Δxij~N (μ Δ tij,σ2Δtij)
Wherein Δ tij=tij-ti(j-1), i=1 ..., n, j=1 ..., mi；
Then according to Maximum Likelihood Estimation Method, Performance Degradation Data Δ xijLikelihood function be
It is by the Maximum-likelihood estimation that likelihood function can acquire parameter μ and σ
It acquiresWithInitial value as parameter μ and σ；
(2) failure probability of life expectancy data；
If the degradation of product is l, i.e., when the performance measurement of product degenerates to l for the first time, product will fail, and product loses
Its out-of-service time of corresponding lifetime data when effect；
If shared M sample products carry out life test to collect lifetime data；If being collected into M lifetime data i.e. M sample
The out-of-service time of product, it is denoted as t1,…,tM, and set t1≤…≤tM；Then obtained using solution in step (1)WithIt presses
The failure probability of following formula life expectancy data tk:
Wherein k=1 ..., M,
(3) Wiener procedure parameter is estimated using the failure probability of lifetime data；
According to all pointsIt is fitted product life distribution curve, i.e., based on the thought of curve matching, is reflected and is calculated using trusted zones
Method, solving optimization model
S.t α > 0, λ > 0
The estimation of inverse Gauss service life profile parameter and λ is obtained, is denoted asWithThe estimation of Wiener procedure parameter μ and σ can then be obtained
For
(4) according to the estimated value of the Wiener procedure parameter acquired in formula (3)WithThe reliablity estimation of t moment product can be obtained
Value are as follows:
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