CN109583039A - A kind of extreme small sample reliability growth test design method - Google Patents
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Abstract
The invention belongs to aeroplane structure design and intensive analysis fields, and in particular to a kind of extreme small sample reliability growth test design method, the first step, in the case where given reliability objectives, inverse goes out logarithmic average service life μ1.Next second step knows the real situation reliability the life value T of test0Virtual augmentation is carried out, to meet Bootstrap method requirement.Then third step can acquire its distribution and mean μ `, the 4th step, finally by μ using Bootstrap method1Compared with μ `, meets error range and export life value T0, otherwise it is iterated, final output meets the life value T of reliability objectives0.Methods herein has as obtained reliability and has known the real situation test life T0And confidence level γ and targeted failure probability R, test life T is acquired, so that the train of mechanism, at confidence level γ, the failure probability in the overhaul life is not more than R.Test life required value is reached, evaluated, which meets reliability growth requirement, and the design method is feasible.
Description
Technical field
The invention belongs to aeroplane structure design and intensive analysis fields, and in particular to a kind of extreme small sample reliability growth examination
Design method is tested, it is suitable for large aerospace mechanical systems.
Background technique
1) for costly and time-consuming large aerospace mechanical system, extreme small sample test, following problem can only be done
Be exactly reliability growth model specified in GJB1407 standard: Duane model and AMSAA model, not being suitable for extreme small sample can
It is assessed by property growth test, and space industry and engine neck are more common in reliability growth test design method research now
Domain and Avionic Products system.The reliability growth test research of aviation field big machinery system is rarely reported.
2) notice that engineering goods service life extreme small sample reliability test evaluation method is quickly grown in recent years simultaneously, Feng Yun
The reliability estimation method based on virtual augmentation of cloud tints professor team research is more and more applied in engineering, and the method is based on
It improves, extreme small sample reliability growth test design method can be obtained.
Summary of the invention
The purpose of the present invention: proposing a kind of extreme small sample reliability growth test design method, is allowed to be suitable for large-scale boat
Empty mechanical system provides guidance for reliability growth test test planning.When large aerospace mechanical system is time-consuming and expensive
Life test when, we can only select to do extreme small sample and know the real situation test.When acquisition is known the real situation test life, we should carry out it
Reliability assessment, and propose reliability growth target, reliability compliance test is then planned, so that verification test service life satisfaction can
By property growth goal.
Methods herein has as obtained reliability and has known the real situation test life T0And confidence level γ and targeted failure probability R,
Test life T is acquired, so that the train of mechanism, at confidence level γ, the failure probability in the overhaul life is not more than R.
Goal of the invention: it by being improved to the extreme small sample reliability estimation method based on engineering experience, solves minimum
There is no the problem of specific theoretical direction in the design of increment reliability growth test.
Technical solution of the present invention:
A kind of extreme small sample reliability growth test design method, the following steps are included:
The first step, in the case where given reliability objectives, inverse goes out logarithmic average service life μ1。
For the fatigue life test reliability assessment problem of the mechanical structured member for the aviation field often studied, largely
The empirical information of engineering test is:
1) fatigue life of the mechanical structured member of aviation field obeys logarithm normal distribution.
If fatigue life variable is T, then claiming T is a lognormal stochastic variable,
T=10Y (1)
Obey logarithm normal distribution, probability density function are as follows:
μ and σ in formula are " logarithmic average " and " logarithm standard deviation ".
The mean value and variance of logarithm normal distribution are respectively as follows:
2) standard deviation substantially 0.17 of the logarithmic fatigue life totality of Normal Distribution.
For obey logarithm normal distribution extreme small sample fatigue life test assess situation, first by logarithm normal distribution with
Machine variable T is converted into normally distributed random variable Y=lgT after taking logarithm, i.e., takes logarithm forming new obedience just test sample
The test sample value Y of state distributioni=lgTi, Y~N (μ, σ at this time2), σ=0.17.
The probability density function of logarithmic fatigue life are as follows:
A confidence level γ is given at this time, so that it may find out corresponding service life lower limit Ylow:
Using service life lower limit as the new mean value service life, distribution function, distribution density function are reconfigured are as follows:
It can find out under 90% confidence level, the failure probability R that flap kinematics device longevity is 16000:
Known parameters σ, γ, R are substituted into formula, Simultaneous Equations can find out the distribution mean μ of logarithmic fatigue life1,
This value can verify the solving result of virtual augmentation Small-Sample Test Circumstances appraisal procedure, to judge whether test number (TN) T meets the requirements.
Next second step knows the real situation reliability the life value T of test0Virtual augmentation is carried out, to meet the side Bootstrap
Method requirement.
By obtaining above, logarithmic fatigue life Y~N (μ, σ2), σ=0.17 can use the symmetrical point sampling method of normal distribution
Carry out the virtual augmentation of sample.
In order to enable the difference of the stochastic behaviour of stochastic behaviour and atom sample that the new increment after virtual augmentation is contained exists
Within engineering allowed band, the process of virtual augmentation needs to meet following two primary condition:
1) the increment mean value after augmentation should be equal with original increment mean value；
2) the increment standard deviation after augmentation should be equal with the increment standard deviation of similarity piece.
It is illustrated with large complicated expensive structure, the life test of train of mechanism for typical case.According to the sample standard deviation of test
ValueIt (as test sample amount n=1, can only approximatively takeT0Once to test resulting sample value) and similarity piece
The distribution form and standard deviation, the sample size of virtual augmentation test specimen, specific practice that test estimation obtains are as follows.
Herein, it will be assumed that original sample amount is n=1.In view of Bootstrap method can be suitable for test well
The Small-Sample Test Circumstances evaluation problem of sample size n >=10, therefore suggest the sample size test specimen from the virtual augmentation of n=1 to n=10.It is false
If the distribution form that similarity piece test estimation obtains is logarithm normal distribution, in order to which the sample for obtaining augmentation is more reasonable, it is proposed that
Virtual augmentation is carried out to sample to lower aprons formula.
In formula, resulting sample value T is once tested0And the value of the increment standard deviation sigma of similarity piece be it is known, Y be increase
The sample value extensively obtained, k are parameter, and m is the quantity (i.e. m=9) for the sample size for needing augmentation.
According to following equation groups:
Can solve sample size is augmented the increment to n=10, meet Bootstrap method use condition at this time.
Then third step can acquire its distribution and mean μ ` using Bootstrap method,
Bootstrap method substantially steps are as follows:
1) original sample Y=y=(y1,y2,...yn) by sequence arrangement from small to large, obtain order statistic y(1),
y(2),…y(n).Y can be obtained with most simple estimation algorithm(i)The cumulative probability value at place is
It is possible thereby to which the empirical cumulative distribution function for constructing original sample is
2) emulation, which generates, obeys empirical cumulative distribution function Fn(y) random sample, i.e. Bootstrap increment.Specific side
Method is as follows:
(1) the equally distributed random number η in [0,1] section is generated；
(2) β=(n-1) η, i=[β]+1 is enabled, wherein [β] is to being rounded under β；
(3)yF=y(i)+(β-i+1)(y(i+1)-y(i)), obtained yFAn as required random sample point；
(4) repeating n times can be obtained a Bootstrap increment Y(1)={ yF (1) 1,yF (1) 2,…yF (1) n}。
3) obtained Bootstrap increment Y is utilized(1)={ yF (1) 1,yF (1) 2,…yF (1) n, construction empirical cumulative is distributed letter
Number Fn *(yF (1)), then show that the Bootstrap of θ estimates with method for parameter estimation
4) it repeats 2) to can be obtained with step n times (N generally takes a biggish numerical value) 3)
5) to obtained in 4)It is for statistical analysis,
The distribution and its characteristic value of unknown parameter θ can be found out.
4th step, finally by μ1Compared with μ `, meets error range and export life value T0, otherwise it is iterated, it is final defeated
Meet the life value T of reliability objectives out0。
Technical effect:
In existing document, the Accuracy of Results of System Reliability Test with Minimum design method about large aerospace mechanical system rarely has report
Road, mentioned method is applied in engineering herein, it was demonstrated that its feasibility.
In aircraft wingflap mechanism reliability growth test, reliability growth examination has been planned with method herein
It tests, test root is satisfactorily completed to test according to charter, has reached test life required value, evaluated, which meets can
Increase by property and require, the design method is feasible.
Detailed description of the invention:
Fig. 1 is extreme small sample reliability growth test design method flow chart.
Specific embodiment:
Extreme small sample reliability growth test design method such as Fig. 1 herein, has been successfully applied to aircraft wing flap
In reliability growth design, reliability growth target is met, it was demonstrated that the feasibility of this method.
Aircraft wingflap mechanism reliability test life value of knowing the real situation is to rise and fall for 30338 times, is determined through engineering experience (specific
It can refer to document: semiempirical appraisal procedure [J] of Feng Yunwen, Huang Wei, Lv Zhenzhou, Song Bifeng, Feng Yuansheng extreme small sample test
Aviation journal, 2004,25 (5): 456-459.), under 90% confidence level, (1600 times in one overhaul life of the wingflap mechanism
Rise and fall) failure probability be 16.02%.
Reliability growth target is now set as 20%, that is, requires after improving mechanism, test is re-started, using the side of this paper
Method acquires the test life met the requirements and rises and falls for 41207 times.
Test is re-started after improving mechanism, 41207 times is successfully made and rises and falls, test stops.Application project passes through again
Testing judgement, (specifically refer to document: the semiempirical of Feng Yunwen, Huang Wei, Lv Zhenzhou, Song Bifeng, Feng Yuansheng extreme small sample test is commented
Estimate method [J] aviation journal, 2004,25 (5): 456-459.), under 90% confidence level, one overhaul life of the wingflap mechanism
The failure probability of interior (1600 times rise and fall) is 12.28%.Meet reliability growth target.
Above-mentioned test proves that this method is feasible, may extend to the extreme small sample reliability growth examination of large aerospace mechanical system
The design tested.
Claims (3)
1. a kind of extreme small sample reliability growth test design method, which comprises the following steps:
Step 1: inverse goes out logarithmic average service life μ in the case where given reliability objectives1；
For the fatigue life test reliability assessment problem of the mechanical structured member for the aviation field often studied, a large amount of engineering
Testing empirical information is:
1) fatigue life of the mechanical structured member of aviation field obeys logarithm normal distribution；
If fatigue life variable is T, then claiming T is a lognormal stochastic variable,
T=10Y(obey logarithm normal distribution, probability density function are as follows:
μ and σ in formula are " logarithmic average " and " logarithm standard deviation "；
The mean value and variance of logarithm normal distribution are respectively as follows:
2) standard deviation substantially 0.17 of the logarithmic fatigue life totality of Normal Distribution；
Extreme small sample fatigue life test for obeying logarithm normal distribution assesses situation, first becomes logarithm normal distribution at random
Amount T is converted into normally distributed random variable Y=lgT after taking logarithm, i.e., takes logarithm to form new obedience normal state point test sample
The test sample value Y of clothi=lgTi, Y~N (μ, σ at this time2), σ=0.17；
The probability density function of logarithmic fatigue life are as follows:
A confidence level γ is given at this time, so that it may find out corresponding service life lower limit Ylow:
Using service life lower limit as the new mean value service life, distribution function, distribution density function are reconfigured are as follows:
It can find out under 90% confidence level, the failure probability R that flap kinematics device longevity is 16000:
Known parameters σ, γ, R are substituted into formula, Simultaneous Equations can find out the distribution mean μ of logarithmic fatigue life1, this value
The solving result of virtual augmentation Small-Sample Test Circumstances appraisal procedure can be verified, to judge whether test number (TN) T meets the requirements；
Step 2: next reliability is known the real situation the life value T of test0Virtual augmentation is carried out, is made with meeting Bootstrap method
With requiring；
According to logarithmic fatigue life Y~N (μ, σ2), σ=0.17 can carry out sample with the symmetrical point sampling method of normal distribution
Virtual augmentation；
Step 3: then can using Bootstrap method acquire its distribution and mean μ,；
Step 4: finally by μ1Compared with μ `, meets error range and export life value T0, otherwise it is iterated, final output is full
The life value T of sufficient reliability objectives0。
2. a kind of extreme small sample reliability growth test design method according to claim 1, which is characterized in that the step
Bootstrap method and step is as follows in rapid three:
1) original sample Y=y=(y1,y2,...yn) by sequence arrangement from small to large, obtain order statistic y(1),
y(2),…y(n)；Y can be obtained with most simple estimation algorithm(i)The cumulative probability value at place is
It is possible thereby to which the empirical cumulative distribution function for constructing original sample is
2) emulation, which generates, obeys empirical cumulative distribution function Fn(y) random sample, i.e. Bootstrap increment；Specific method is such as
Under:
(1) the equally distributed random number η in [0,1] section is generated；
(2) β=(n-1) η, i=[β]+1 is enabled, wherein [β] is to being rounded under β；
(3)yF=y(i)+(β-i+1)(y(i+1)-y(i)), obtained yFAn as required random sample point；
(4) repeating n times can be obtained a Bootstrap increment Y(1)={ yF (1) 1,yF (1) 2,…yF (1) n}；
3) obtained Bootstrap increment Y is utilized(1)={ yF (1) 1,yF (1) 2,…yF (1) n, construct empirical cumulative distribution function Fn *
(yF (1)), then show that the Bootstrap of θ estimates with method for parameter estimation
4) it repeats 2) and step n times 3), N generally takes a biggish numerical value；It can be obtained
5) to obtained in 4)It is for statistical analysis
Find out the distribution and its characteristic value of unknown parameter θ.
3. a kind of extreme small sample reliability growth test design method according to claim 1, which is characterized in that in order to make
The difference of the stochastic behaviour of stochastic behaviour and atom sample that is contained of new increment after virtual augmentation engineering allowed band it
Interior, the process of virtual augmentation needs to meet following two primary condition:
1) the increment mean value after augmentation should be equal with original increment mean value；
2) the increment standard deviation after augmentation should be equal with the increment standard deviation of similarity piece；
It is illustrated with large complicated expensive structure, the life test of train of mechanism for typical case；According to the sample average of test
As test sample amount n=1, can only approximatively takeT0Once to test resulting sample value；And similarity piece test is estimated
It counts obtained distribution form and standard deviation, the sample size of virtual augmentation test specimen, specific practice is as follows；
Herein, it will be assumed that original sample amount is n=1；In view of Bootstrap method can be suitable for test sample well
The Small-Sample Test Circumstances evaluation problem of n >=10 is measured, therefore suggests the sample size test specimen from the virtual augmentation of n=1 to n=10；Assuming that class
It is logarithm normal distribution like the distribution form that part test estimation obtains, in order to which the sample for obtaining augmentation is more reasonable, it is proposed that
Lower aprons formula carries out virtual augmentation to sample；
In formula, resulting sample value T is once tested0And the value of the increment standard deviation sigma of similarity piece be it is known, Y obtains for augmentation
Sample value, k is parameter, and m is the quantity for needing the sample size of augmentation, i.e. m=9；
According to following equation groups:
Can solve sample size is augmented the increment to n=10, meet Bootstrap method use condition at this time.
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Application publication date: 20190405 |