CN103488826B - Amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model - Google Patents

Abstract

The invention discloses a kind of amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model, comprise following step: step 1, select the experience acceleration model of corresponding accelerated life test; Step 2, set up the amount of degradation distributed constant acceleration model of amount of degradation distributed constant and stress relation; Step 3, the amount of degradation distributed constant value of utilizing gained amount of degradation distributed constant acceleration model to extrapolate under target stress. The present invention adopts and is carried out modeling in accelerated life test field by the experience acceleration model of large quantity research and application attestation, can effectively utilize correlation test information in product research process and the Test Information of Related product, improve the credibility of result of the test. The present invention, taking model inference as basis, has avoided under Small Sample Size, and while adopting merely homing method to describe distributed constant and stress relation, accuracy is difficult to the problem ensureing.

Description

Amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model

Technical field

The present invention relates to a kind of amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model, belong to accelerated degradation testTechnical field.

Background technology

In the time that suffered stress is normal working stress, the performance degradation of high reliability long life product is process very slowly. At thisUnder the condition of kind, expect to obtain enough degraded datas, certainly will will experience the longer time and pay corresponding manpower and materials cost. ForWithin a short period of time obtain the data volume that analyzing and processing needs, in laboratory environment, adopt that to improve product suffered stress harshThe method of level, the degenerative process of expedite product, be current solution high reliability long life prediction and evaluation problem focus direction itOne. Develop into and accelerate stress degradation experiment from the degradation experiment of normal applied stress, test period and relevant support expense cost obtainArrive significantly and reduced. Shorten in product development cycle facilitates and change at this, corresponding data processing also becomesObtain more difficult. The degraded data will speed up under stress is transformed under regular service conditions, is accelerate degraded data processing mainOne of difficult point. Bibliography [1] (Zhao Jianyin, Sun Quan, Peng Baohua, Zhou Jinglun. based on the reliability of accelerated degradation test dataAnalyze, electron mass, 2005 (7), 30-33) in acceleration degeneration equation concept has been proposed, suppose that amount of degradation function exists derivative,Taking the Arrhenius in reactivity model as basis, acceleration degeneration equation and logarithmic form thereof are provided. But, existing acceleration mouldIn type, except reactivity model, also has application very extensively against experience acceleration model (bibliography [2]: Huang such as power rate modelsGraceful, Jiang Tongmin. in accelerated life test, add up acceleration model summary, equipment Environmental Engineering, 2010,7 (4), 57-62). ByBe not taking reaction rate as basis in experience acceleration models such as contrary power rates, in bibliography [1], accelerate the modeling of degeneration equationJourney is not also suitable for experience acceleration model.

For this problem, taking the experience acceleration model very ripe in accelerated life test field as basis, set up reflection hereinThe amount of degradation distributed constant acceleration model of amount of degradation distributed constant and stress relation. In model inference process, with widely used contraryPower rate model is example, sets up corresponding numerical relationship model, and the amount of degradation distributed constant under extrapolation normal stress is convenient to accelerate to move backChange the practical application of test.

Summary of the invention

The object of the invention is the relationship modeling technical problem in order to solve amount of degradation distributed constant and stress in accelerated degradation test,A kind of amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model is proposed.

Described method comprises the steps:

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

(2) set up the amount of degradation distributed constant acceleration model of amount of degradation distributed constant and stress relation;

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

The invention has the advantages that:

(1) adopt and carried out modeling in accelerated life test field by the experience acceleration model of large quantity research and application attestation, canEffectively to utilize correlation test information in product research process and the Test Information of Related product, improve the credible of result of the testProperty;

(2) avoided under Small Sample Size, while adopting merely homing method to describe distributed constant and stress relation, accuracy is difficult toThe problem ensureing.

Brief description of the drawings

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

Detailed description of the invention

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 distributed constant modeling Extrapolation method based on experience acceleration model, flow process as shown in Figure 1, toolBody implementation method is as follows:

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

For experience acceleration model, based on engineer, properties of product long-term observation summed up and proposed, and in practical applicationIn obtained the confirmation of great number tested data. For example contrary power rate model description the relation between voltage or pressure and life of product,Coffin-Manson model description the relation between temperature cycles stress and life of product. In hypothesis test process, product is executedThe acceleration stress adding 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, often getsVoltage.

Step 2, set up the amount of degradation distributed constant acceleration model of amount of degradation distributed constant and stress relation;

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

ξ＝f(D_f)^-1(2)

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

In fact, the determined value on degradation failure threshold value is not strict, relevant with actual demand. For example, for critical product or portionThe degeneration life-span of part, in order to reduce the risk of product failure, improve margin of safety, it is more conservative that degradation failure threshold value can be determined;Otherwise, can be decided to be more optimistic index. Degradation failure, also referred to as " soft failure ", was lost efficacy with demblee form, i.e. " hard failure "Compare, in the certainty in " life-span ", have certain difference. When degradation failure changes of threshold, " life-span " of degradation failure also withVariation. Therefore, under theoretical case, 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_fRepresent degradation failure threshold value D_fCan in degeneration value is positive scope, change continuously, variable t represents correspondingDegeneration life-span ξ be also continually varying time value.

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

f(d_f)^-1＝Av^-C(4)

In formula, no longer include time dependent amount. And d_fIn fact be just selected as the degeneration value of " degradation failure threshold value ", withGeneral amount of degradation has the identical domain of definition, might as well replace d with general amount of degradation M_f, to make the derivation of equation more straightSee, obtain:

f(M)^-1＝Av^-C,M＝d_f(5)

Formula (5) is taken the logarithm:

ln(f(M)^-1)＝lnA-Clnv(6)

From formula (6), can find out the functional transformation ln (f (M) of general amount of degradation M^-1) and the natural logrithm ln ν of stress between beLinear relationship, coefficient C wherein and lnA(or other constant terms) can obtain by the linear regression to data. Due to allThe distributed constants such as value μ, scale parameter η are the index that embodies data general characteristic, and its meaning has embodied the degeneration of " totally "Measure, belong to the category of general amount of degradation, therefore itself and the same coincidence formula of relation (5) of stress and the model of formula (6), i.e. formula (5)With formula (6) described the relation of amount of degradation distributed constant and stress, this conclusion is applicable to formula (9) and formula below too(10)。

The present invention is taking contrary power rate model as example, and the amount of degradation distributed constant acceleration model having provided based on experience acceleration model was derivedJourney. For other experience acceleration models, suppose that its life-span acceleration model has following common version:

WhereinFor the function of stress S, be the generic representation form on experience acceleration model equation right side. With derivation phase aboveWith, in the time of t=ξ, in conjunction with formula (7) and formula (3), there are formula (4) and the corresponding universal expression form of formula (5):

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

Step 3, the amount of degradation distributed constant value of utilizing gained amount of degradation distributed constant acceleration model to extrapolate under target stress;

Taking contrary power rate model as example, obtain performance degenrate function f (.) according to Degradation path, application of formula (6) adopts to be accelerated under stress notWith the data of amount of degradation distributed constant under stress, return the parameters C obtaining in i moment acceleration model formula_iAnd lnA_i(or itsHis constant term). Under the normal stress in any i momentExtrapolation, can be by normal stress value ν₀Substitution outer apply-official nowFormula:

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

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 applying is voltage stress, and the 90h moment surveysObtaining the Mean Parameters that under each stress, amount of degradation distributes is: (7.5V, 0.14750), (7.0V, 0.0652), (6.7V, 0.0316). NotAffect in the situation of method validation, the magnitude of Mean Parameters has been done relevant treatment, and unit omits. The degeneration initial value of this productBe 0, Degradation path function f (.) has the form of f (t)=at. Adopt below under the extracting method extrapolation 6.5V of institute of the present invention normal stressAverage.

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

Step 2, set up the amount of degradation distributed constant acceleration model of amount of degradation distributed constant and stress relation;

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

Step 3, the amount of degradation distributed constant value of utilizing gained amount of degradation distributed constant acceleration model to extrapolate under target stress;

For the data in 90h 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

lnμ₉₀＝ln(aA₉₀)-C₉₀lnv(12)

Through linear regression, try to achieve

C₉₀=-13.5003,ln(aA₉₀)=-29.0834

By ν₀=6.5 substitution formula (12) obtain the average under 6.5V normal stress。

Claims (1)

1. the amount of degradation distributed constant modeling Extrapolation method based on experience acceleration model, is characterized in that, comprises followingStep:

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;

For the contrary power rate model representation of accelerated life test be now:

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 distributed constant acceleration model of amount of degradation distributed constant and stress relation;

Use D_fThe degradation failure threshold value that represents product, the life characteristics of product is:

ξ＝f(D_f)^-1(2)

In formula, f (.) is the universal expression formula of performance degradation function, adopts the form of implicit function herein;

Under theoretical case, 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_fRepresent degradation failure threshold value D_fIn degeneration value is positive scope, change continuously, variable t represents to move back accordinglyChanging life-span ξ is also continually varying time value;

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

f(d_f)^-1＝Av^-C(4)

With general amount of degradation M replacement d_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 amount of degradation distributed constant and relation stress;

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

WhereinFor the function of stress S, in the time of t=ξ, in conjunction with formula (7) and formula (3), there are formula (4) and formula (5) correspondingUniversal expression form:

Step 3, the amount of degradation distributed constant value of utilizing gained amount of degradation distributed constant acceleration model to extrapolate under target stress;

Obtain degenrate function f (.) according to Degradation path, amount of degradation distributed constant under different stress under application of formula (6) employing acceleration stressData, return and obtain parameters C in i moment acceleration model formula_iAnd lnA_i, to moving back under the normal stress in any i momentChange amountExtrapolation, by normal stress value ν₀Substitution extrapolation formula now:

$\ln \left(f{\left(M_i^0\right)}^{-1}\right)={\mathrm{lnA}}_i-C_i{\mathrm{lnv}}_0---\left(10\right)$

Solve and obtain.