CN103488826A - Experience acceleration model based degradation amount distribution parameter modeling and extrapolating method - Google Patents

Abstract

The invention discloses an experience acceleration model based degradation amount distribution parameter modeling and extrapolating method. The method includes the following steps: firstly, selecting an experience acceleration model corresponding to an accelerated life test; secondly, establishing a degradation amount distribution parameter acceleration model of a relation of degradation amount distribution parameters and stress; thirdly, extrapolating a degradation amount distribution parameter value under target stress by the aid of the degradation amount distribution parameter acceleration model. The experience acceleration model which already undergoes a large amount of research and is proved by application in the field of accelerated life tests is adopted for modeling, relevant test information in the product research process and test information of relevant products can be utilized effectively, and credibility of test results is improved. On the basis of model extrapolation, the problem that accuracy is difficult to guarantee when a regression method is purely adopted to describe the relation of the distribution parameter and the stress under the circumstance of small samples is avoided.

Description

Amount of degradation distribution parameter modeling Extrapolation method based on the experience acceleration model

Technical field

The present invention relates to a kind of amount of degradation distribution parameter modeling Extrapolation method based on the experience acceleration model, belong to the accelerated degradation test technical field.

Background technology

When suffered stress, for normal operation during stress, the performance degradation of high reliability long life product is process very slowly.Under this condition, expectation obtains enough degraded datas, certainly will will experience the longer time and pay corresponding manpower and materials cost.The data volume needed in order to obtain analyzing and processing within a short period of time, in laboratory environment, adopt the method that improves the harsh level of the suffered stress of product, the degenerative process of expedite product, be one of focus direction of current solution high reliability long life prediction and evaluation problem.Develop into acceleration stress degradation experiment from the degradation experiment of normal applied stress, test period and relevant support expense cost have obtained decrease.And, when this changes into and shortens product development cycle and facilitate, corresponding data are processed and are also become more difficult.The degraded data will speed up under stress is transformed under regular service condition, is one of Major Difficulties accelerated the degraded data processing.List of references [1] (Zhao Jianyin, Sun Quan, Peng Baohua, Zhou Jinglun. the fail-safe analysis based on the accelerated degradation test data, electron mass, 2005 (7), acceleration degeneration equation concept has been proposed 30-33), suppose that there is derivative in the amount of degradation function, the Arrhenius of take in the reaction rate model, as basis, has provided acceleration degeneration equation and logarithmic form thereof.Yet, in existing acceleration model, except the reaction rate model, also have application very extensively against the experience acceleration models such as power rate model (list of references [2]: yellow graceful, Jiang Tongmin. statistics acceleration model summary in accelerated life test, equipment Environmental Engineering, 2010,7 (4), 57-62).Because the experience acceleration models such as contrary power rate are not that to take reaction rate be basis, the modeling process that accelerates the degeneration equation in list of references [1] also is not suitable for the experience acceleration model.

For this problem, the very ripe experience acceleration model in the accelerated life test field be take in this paper is basis, sets up the amount of degradation distribution parameter acceleration model of reflection amount of degradation distribution parameter and stress relation.In the model inference process, the widely used contrary power rate model of take is example, sets up corresponding numerical relationship model, and the amount of degradation distribution parameter under the extrapolation normal stress, be convenient to the practical application of accelerated degradation test.

Summary of the invention

The objective of the invention is, in order to solve the relationship modeling technical matters of amount of degradation distribution parameter and stress in accelerated degradation test, to propose a kind of amount of degradation distribution parameter modeling Extrapolation method based on the experience acceleration model.

Described method comprises the steps:

(1) select the experience acceleration model of corresponding accelerated life test;

(2) set up the amount of degradation distribution parameter acceleration model of amount of degradation distribution parameter and stress relation;

(3) utilize the amount of degradation distribution parameter value under gained amount of degradation distribution parameter acceleration model extrapolation target stress.

The invention has the advantages that:

(1) adopt and carried out modeling in the accelerated life test field by the experience acceleration model of large quantity research and application attestation, can effectively utilize correlation test information in the product research process and the Test Information of Related product, improved the credibility of test findings;

(2) avoided under Small Sample Size, while adopting merely homing method to describe distribution parameter and stress relation, accuracy is difficult to the problem guaranteed.

The accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of amount of degradation distribution parameter modeling Extrapolation method based on the experience acceleration model, flow process as shown in Figure 1, and specific implementation method is as follows:

Step 1, select the experience acceleration model of corresponding accelerated life test;

For the experience acceleration model, be based on the slip-stick artist and the properties of product long-term observation summed up and proposed, and obtained in actual applications the confirmation of great number tested data.For example contrary power rate model description the relation between voltage or pressure and life of product, the Coffin-Manson model description relation between temperature cycles stress and life of product.In the hypothesis test process, the acceleration stress that product is applied is voltage stress, and corresponding acceleration model is selected contrary power rate model.

Contrary power rate model representation for accelerated life test is:

ξ＝Av ^-C (1)

In formula: ξ is certain life characteristics; A is a normal number; C is a normal number relevant with activation energy; V is stress, and normal power taking is pressed.

Step 2, set up the amount of degradation distribution parameter acceleration model of amount of degradation distribution parameter and stress relation;

For degenerating the life-span, be commonly defined as product performance index from the degeneration initial time to the time span that reaches defined threshold and experience, this defined threshold is the degradation failure threshold value of product, usually uses D _fmean.

ξ＝f(D _f) ^-1 (2)

In formula, the universal expression formula that f (.) is the performance degradation function, adopt the form of implicit function herein, so that the expression in formulation process.

In fact, the determined value on the degradation failure threshold value is not strict, relevant with actual demand.For example, for the degeneration life-span of critical product or parts, in order to reduce the risk of product failure, improve margin of safety, it is more conservative that the degradation failure threshold value can be determined; Otherwise, can be decided to be more optimistic index.Degradation failure is also referred to as " soft failure ", with demblee form, lost efficacy, " hard failure " compare, certain difference is arranged on the determinacy in " life-span ".During the degradation failure changes of threshold, " life-span " of degradation failure also changes thereupon.Therefore, under theoretical case, the degradation failure threshold value can get arbitrarily on the occasion of, correspondingly have:

t＝f(d _f) ^-1,d _f≥0 (3)

In formula, variable d _fmean degradation failure threshold value D _fcan in the degeneration value is positive scope, change continuously, the variable t life-span ξ that means to degenerate accordingly is also continually varying time value.

Contrary power rate model description the relation of life of product and suffered stress, with the variation of life of product, do not change.So same life-span constantly, during t=ξ, formula (1) and formula (2) can be combined into:

f(d _f) ^-1＝Av ^-C (4)

No longer include time dependent amount in formula.And d _fin fact just be selected as the degeneration value of " degradation failure threshold value ", with general amount of degradation, there is identical field of definition, might as well replace d with general amount of degradation M _f, so that the derivation of equation is more directly perceived, obtain:

f(M) ^-1＝Av ^-C,M＝d _f (5)

Formula (5) is taken the logarithm:

ln(f(M) ^-1)＝lnA-Clnv (6)

Can find out the functional transformation ln of general amount of degradation M (f (M) from formula (6) ^-1) and the natural logarithm ln ν of stress between be linear relationship, coefficient C wherein and lnA(or other constant terms) can obtain by the linear regression to data.Because the distribution parameters such as average μ, scale parameter η are the index that embodies the data general characteristic, its meaning has embodied the amount of degradation of " totally ", the category that belongs to general amount of degradation, therefore itself and the same coincidence formula of relation (5) of stress and the model of formula (6), be the relation that formula (5) and formula (6) have been described amount of degradation distribution parameter and stress, this conclusion is applicable to formula (9) and formula (10) hereinafter too.

It is example that the present invention be take against power rate model, has provided the amount of degradation distribution parameter acceleration model derivation based on the experience acceleration model.For other experience acceleration models, suppose that its life-span acceleration model has following common version:

Wherein

for the function of stress S, be the generic representation form on experience acceleration model equation right side.Identical with the front derivation, when t=ξ, in conjunction with formula (7) and formula (3), formula (4) and the corresponding universal expression form of formula (5) are arranged:

Model parameter to be estimated in formula (9) can be carried out proper transformation with reference to formula (6) in conjunction with concrete equation form, by the simple regression method, just can obtain, and does not repeat them here simultaneously.

Step 3, utilize the amount of degradation distribution parameter value under gained amount of degradation distribution parameter acceleration model extrapolation target stress;

Take against power rate model is example, according to Degradation path, obtains performance degenrate function f (.), and under application of formula (6) employing acceleration stress, the data of amount of degradation distribution parameter under different stress, return the parameters C obtained in i moment acceleration model formula _iand lnA _i(or other constant terms).Under normal stress to any i moment extrapolation, can be by normal stress value ν ₀substitution extrapolation formula now:

$\ln \left(f{\left(M_i^0\right)}^{-1}\right)=\ln A_i-C_i\ln v_0---\left(10\right)$

Solve and obtain.Herein, the extrapolation of other experience acceleration models solves identical therewith.

Embodiment 1: in the accelerated degradation test of certain product, the acceleration stress applied is voltage stress, and the Mean Parameters that under 90h measured each stress of the moment, amount of degradation distributes is: (7.5V, 0.14750), (7.0V, 0.0652), (6.7V, 0.0316).In the situation that do not affect method validation, the magnitude of Mean Parameters has been done relevant treatment, and unit omits.The degeneration initial value of this product is 0, and Degradation path function f (.) has the form of f (t)=at.Below adopt the average under the extracting method extrapolation 6.5V of institute of the present invention normal stress.

Step 1, select the experience acceleration model of corresponding accelerated life test;

Because the stress that product is applied is voltage stress, the contrary power rate model in the experience acceleration model is applicable to describing the relation of this life of product and stress, and selecting contrary power rate model is accelerated life model, and its expression formula is as shown in formula (1).

Step 2, set up the amount of degradation distribution parameter acceleration model of amount of degradation distribution parameter and stress relation;

The modeling process of amount of degradation distribution parameter acceleration model, referring to the content in step 2 above, no longer repeats herein.

Step 3, utilize the amount of degradation distribution parameter value under gained amount of degradation distribution parameter acceleration model extrapolation target stress;

For the 90h data in the moment, by Degradation path function f (.) substitution formula (5), have

$a^{-1}{\mathrm{\μ}}_{90}=A_{90}{v}^{-C_{90}}---\left(11\right)$

After taking the logarithm, conversion obtains

lnμ ₉₀＝ln(aA ₉₀)-C ₉₀lnv (12)

Through linear regression, try to achieve

C ₉₀=-13.5003,ln(aA ₉₀)=-29.0834

By ν ₀=6.5 substitution formula (12) obtain the average under the 6.5V normal stress .

Claims (1)

1. the amount of degradation distribution parameter modeling Extrapolation method based on the experience acceleration model, is characterized in that, comprises following step:

Step 1, select the experience acceleration model of corresponding accelerated life test;

If the acceleration stress that product is applied is voltage stress, select contrary power rate model;

Now the contrary power rate model representation for accelerated life test is:

ξ＝Av ^-C (1)

In formula: ξ is certain life characteristics; A is a normal number; C is a normal number relevant with activation energy; V is stress; Step 2, set up the amount of degradation distribution parameter acceleration model of amount of degradation distribution parameter and stress relation;

Use D _fmean the degradation failure threshold value of product, the life characteristics of product is:

ξ＝f(D _f) ^-1 (2)

The universal expression formula that in formula, f (.) is the performance degradation function, adopt the form of implicit function herein;

Under theoretical case, the degradation failure threshold value get arbitrarily on the occasion of, correspondingly have:

t＝f(d _f) ^-1,d _f≥0 (3)

In formula, variable d _fmean degradation failure threshold value D _fin the degeneration value is positive scope, change continuously, the variable t life-span ξ that means to degenerate accordingly is also continually varying time value;

Contrary power rate model description the relation of life of product with suffered stress, with the variation of life of product, do not change, so, in the same moment in life-span, during t=ξ, formula (1) and formula (2) are combined into:

f(d _f) ^-1＝Av ^-C (4)

Replace d with general amount of degradation M _f, have:

f(M) ^-1＝Av ^-C,M＝d _f (5)

Formula (5) is taken the logarithm:

ln(f(M) ^-1)＝lnA-Clnv (6)

Formula (5) and formula (6) have been described the amount of degradation distribution parameter and relation stress;

Suppose that the life-span acceleration model has following common version:

Wherein

for the function of stress S, when t=ξ, in conjunction with formula (7) and formula (3), formula (4) and the corresponding universal expression form of formula (5) are arranged:

Step 3, utilize the amount of degradation distribution parameter value under gained amount of degradation distribution parameter acceleration model extrapolation target stress;

Obtain degenrate function f (.) according to Degradation path; the data of amount of degradation distribution parameter under different stress under application of formula (6) employing acceleration stress; recurrence obtains the parameter in i moment acceleration model formula, to amount of degradation under the normal stress in any i moment

extrapolation, by normal stress value v ₀substitution extrapolation formula now:

$\ln \left(f{\left(M_i^0\right)}^{-1}\right)=\ln A_i-C_i\ln v_0---\left(10\right)$

Solve and obtain.

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