CN107122547A - Sophisticated testing uncertainty evaluation method based on Bayes principle - Google Patents
Sophisticated testing uncertainty evaluation method based on Bayes principle Download PDFInfo
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Abstract
The present invention relates to a kind of sophisticated testing uncertainty evaluation method based on Bayes principle, determine that sophisticated testing is measured and major influence factors；Obtain the probability density function of sophisticated testing influence factor；Test sampling is carried out according to the probability density function of influence factor using Latin Hypercube Sampling method, the experimental design table of influence factor is obtained, is tested according to the parameter of design table, obtain the result of sophisticated testing under each input parameter；The partial data of result of the test is used as current measurement sample as priori sample, another part；Calculate the average of priori sample and the standard deviation of average, and the current average and standard deviation for measuring sample；Interval is included by the estimation of the measured true value of Posterior distrbutionp calculating, standard uncertainty and correspondingly comprising probability, thus result of calculation is used as uncertainty evaluation.The method can provide it and test uncertainty, experimental result be evaluated, so as to formulate experiment Innovatation scheme while sophisticated testing provides result of the test.
Description
Technical field
The present invention relates to a kind of mechanical engineering experiment, more particularly to a kind of sophisticated testing based on Bayes principle is not known
Spend assessment method.
Background technology
With the development of mechanical industry, requirement more and more higher of the people to product quality, therefore many products are both needed to progress
Correlation test examines the qualification and reliability of product.And it is all sophisticated testing that these experiments are a lot, sophisticated testing it is general
Be characterized in result of the test influence factor it is numerous, the small variations of each factor will all cause the uncertainty of result of the test, if examination
Testing the uncertainty of result does not have clear and definite module, and the confidence level for making result of the test is reduced.It is directed to accordingly, it would be desirable to study
Sophisticated testing result uncertainty analysis method, to improve the confidence level of result of the test.
Uncertainty evaluation method conventional at present be by《Uncertainty of measurement guide》(GUM) the A classes and B classes proposed is commented
It is fixed.But when measurement model is complicated nonlinear system, and sample number it is few when, using GUM methods to uncertainty of measurement
Carrying out evaluation will cause result inaccurate.And the Evaluation of Uncertainty method based on Bayes principle can make full use of existing letter
Breath, sample information, posterior infromation etc., statistical inference is set up on the basis of experiment distribution, is particularly suitable for use in small sample experiment
The evaluation of uncertainty.Therefore for the evaluation of Complex Nonlinear System test measurement uncertainty, using former based on Bayes
The test measurement Evaluation of Uncertainty of reason will obtain more rational result.
The content of the invention
The problem of product quality of reliability of sophisticated testing the present invention be directed to verify to(for) sophisticated testing to be relied on,
A kind of sophisticated testing uncertainty evaluation method based on Bayes principle is proposed, the same of result of the test is provided in sophisticated testing
When, it can be provided and test uncertainty, and experimental result is evaluated, so as to formulate experiment Innovatation scheme.
The technical scheme is that：A kind of sophisticated testing uncertainty evaluation method based on Bayes principle, specifically
Comprise the following steps：
1), determine that sophisticated testing is measured Y, and major influence factors X=[x1,x2,...,xn]；
2) sophisticated testing influence factor x, is obtainediProbability density function gxi(ξi), ξiFor the measurement of influence factor
Value；
3), using probability density function gx of the Latin Hypercube Sampling method according to influence factori(ξi) carry out experiment take out
Sample, obtains the experimental design table D of influence factorn, tested according to the parameter of design table, obtain complicated examination under each input parameter
The result Y testedi；
4), the uncertainty of sophisticated testing is evaluated based on Bayes principle：
4.1) with step 3) result of the test YiPartial data as priori sample, another part is used as current measurement sample
This；
4.2) mean μ of priori sample is calculated0With the standard deviation τ of average, and current measurement sample averageAnd standard
Poor s；
4.3) estimation of measured true value is calculated using shown formula
Wherein n is current measurement total sample number；
4.4) standard uncertainty σ is calculated using shown formula
4.5) by the estimation of obtained measured true valueIt is corresponding with standard uncertainty σ calculating to include area comprising Probability p
Between [ylow,yhigh], wherein ylowAnd yhighIt is respectively minimum value and maximum in interval to calculate；
5) step 4.4, is exported) and 4.5) result is used as uncertainty evaluation.
The beneficial effects of the present invention are：Sophisticated testing uncertainty evaluation method of the invention based on Bayes principle,
While sophisticated testing provides result of the test, it can be provided and test uncertainty, experimental result is evaluated according to this,
So as to formulate experiment Innovatation scheme.Guaranteed quality requires the quality of high product while improving examination and test of products level.
Brief description of the drawings
Fig. 1 is the sophisticated testing uncertainty evaluation method flow diagram of the invention based on Bayes principle；
Fig. 2 is that the present invention whips experiment major influence factors schematic diagram；
Fig. 3 is H points X-axis coordinate probability density function figure of the present invention；
Fig. 4 is H points Z axis coordinate probability density function figure of the present invention；
Fig. 5 is head post gap BS probability density function figures of the present invention；
Fig. 6 is BA probability density function figures in backrest angle of the present invention；
Fig. 7 is F1 of the present invention distribution probability density function figure；
Fig. 8 is F2 of the present invention distribution probability density function figure.
Embodiment
Sophisticated testing uncertainty evaluation method flow diagram as shown in Figure 1 based on Bayes principle, concrete scheme is as follows：
1st, determine that sophisticated testing is measured Y, and major influence factors X=[x1,x2,...,xn]。
2nd, sophisticated testing influence factor x is obtainediProbability density function gxi(ξi), ξiFor the measurement of influence factor
Value.
3rd, using probability density function gx of the Latin Hypercube Sampling method according to influence factori(ξi) test sampling is carried out,
Obtain the experimental design table D of influence factorn, tested according to the parameter of design table, obtain sophisticated testing under each input parameter
Result Yi。
4th, the uncertainty of sophisticated testing is evaluated based on Bayes principle：
4.1 with step 3 result of the test YiPartial data as priori sample, another part is used as current measurement sample.
4.2 calculate the mean μ of priori sample0With the standard deviation τ of average, and current measurement sample averageAnd mark
Quasi- difference s.
4.3 calculate the estimation of measured true value using shown formula (1)
Wherein n is current measurement total sample number
4.4 calculate standard uncertainty σ using shown formula (2)
4.5 by the estimation of obtained measured true valueIt is corresponding with standard uncertainty σ calculating to include area comprising Probability p
Between [ylow,yhigh], wherein ylowAnd yhighIt is respectively minimum value and maximum in interval to calculate.
5th, 4.4 and 4.5 results of output are used as uncertainty evaluation.
The present invention whips test scores uncertainty evaluation with the automotive seat of a certain model and illustrated, and specific steps are such as
Under：
(1) determine to whip experiment major influence factors.
Experiment major influence factors schematic diagram is whipped as shown in Figure 2, is chosen on whipping test scores influence large effect
Factor, includes the backrest angle BA of seat parameter itself, the neck pretightning force F1 and neck pretightning force F2 of dummy parameter itself, installs
The dummy H points of parameter are with respect to pivot point X-axis coordinate difference Hx, dummy H points with respect to pivot point Z axis coordinate difference Hz and head post gap BS.
(2) determination of each influence factor probability density distribution.
Each input parameter is counted according to historical data, H points X-axis coordinate probability density distribution as shown in Figure 3 is drawn
Functional arrangement, H as shown in Figure 4 point Z axis coordinate probability density functions figure, head post gap BS probability density distributions as shown in Figure 5
Functional arrangement, three meets normal distribution, and BA probability density function figures in backrest angle as shown in Figure 6 meet rectangle point
Cloth.
Shown in the general expression of normal distyribution function such as formula (3), it is designated asIts probability density function is normal state
The desired value θ of distribution determines its position, its standard deviationDetermine the amplitude of distribution.
In this example, standard value of the dummy H points with respect to pivot point X-axis coordinate difference Hx is 216.06, and dummy H points are relative
Pivot point Z axis coordinate difference Hz standard value is 53.78, and head post gap BS standard value is 27.After handling data
Draw H point X-axis coordinate, the Z axis coordinate of H points, head post gap, the probability density function at backrest angle respectively such as formula (4)-(7)
It is shown.
Hx~N (216.21,1.23782) (4)
Hz~N (46.30,4.05272) (5)
BS~N (26.89,0.73772) (6)
BA~U (14.5,19.5) (7)
Dummy neck pretightning force is due to no sensor, it is impossible to drawn by historical data, can only be imitative by rating test
Really show that it is distributed.Multiple Calibration Simulation experiment is carried out by the value for changing F1 and F2, drawing dummy calibration, qualified condition is
F1 span will in the range of (33.51,82.68) N, F2 span will (99.48,166.04) N scope
It is interior.The probability density distribution for counting each output item according to rating test historical data meets normal distribution, thus reasons out
Adjustable parameter dummy neck pretightning force F1 and F2 in calibration experiment also complies with normal distribution law.If in view of F1 95%
Confidential interval be (33.51,82.68), F2 95% confidential interval is (99.48,166.04), can obtain F1 and F2 point
Cloth probability density function is expressed as (8) and (9), and correspondence probability distributing density function is as shown in Figure 7 and Figure 8.
F1~N (58.095,12.5432) (8)
F2~N (132.76,16.982) (9)
(3) experiment is whipped in Latin Hypercube Sampling method design.
The purpose for whipping experiment is the protecting effect for testing seat to occupant's neck, and for the seat of a certain concrete model
The number of times tested it is less, and the inaccurate of result will be caused by directly carrying out Evaluation of Uncertainty using test result.Cause
This need to replace physical test to whip experiment uncertainty to the model seat to carry out the method for lot of experiments using finite element
Evaluated.Now experimental design parameter should meet probability density distribution, therefore using Latin Hypercube Sampling method to design
Parameter is sampled selection, and the methods of sampling belongs to stratified sampling, and obtained sample meets its probability density distribution, and can be covered with
Whole design space.The test number (TN) n chosen in this example is 50 times, and sampling results sees attached list 1, by the design of subordinate list 1
The result of the test that parameter is obtained, whips experiment finite element simulation appraisal result as shown in table 2.
Table 1
Table 2
(4) uncertainty evaluation based on Bayes principle.
Bayes method is a kind of estimating method based on statistical theory, and it can make full use of existing information, sample letter
Breath, posterior infromation etc., set up Bayes's uncertainty evaluation model, obtain testing uncertainty finally by Posterior distrbutionp.Tool
Body estimation steps are as follows：
4.1) choose l-G simulation test before 30 groups as priori sample, rear 20 groups of data are used as current sample.
4.2) average of priori sample is calculatedWith the standard deviation of averageDue to commenting
Point result belongs to normal distribution, then the priori density function of mean μ is：
In formula：nfThe sum of sample, Y are measured for priorii fThe measured value of sample is measured for priori.
4.3) average of current sample is calculatedAnd standard deviationThe then joint of current sample
Density function (likelihood function) is
In formula：N is the sum of current measurement sample, YjFor the measured value of current measurement sample.
4.4) Posterior distrbutionp can be obtained according to Bayesian inference h (μ | Y) ∝ p (μ) L (μ | Y)
In formula
Thus it can be calculated the estimation of measured true valueAnd standard uncertainty σ.
4.5) by the estimation of obtained measured true valueIt is corresponding with standard uncertainty σ calculating to include Probability p=1- α's
Include interval [ylow,yhigh]。
WhereinZα/2It can be obtained by query criteria normal distyribution function table,
Wherein Zα/2Critical value is represented in Standard Normal Distribution table, α is quantile.
(5) uncertainty evaluation result.
The result of the test of evaluation project and subordinate list 2 calculates the mean μ of priori sample according to step (4)0=
3.8573 and standard deviation τ=0.0626 of average；The average of current sampleWith standard deviation s=0.2520；Finally count
The estimate of the Posterior distrbutionp calculatedWith standard uncertainty σ, and obtain corresponding to it is different comprising Probability p comprising interval
[ylow,yhigh], result is as shown in table 3 below whips test scores analysis on Uncertainty knot based on bayesian theory for concrete analysis
Really.
Table 3
Claims (1)
1. a kind of sophisticated testing uncertainty evaluation method based on Bayes principle, it is characterised in that specifically include following step
Suddenly：
1), determine that sophisticated testing is measured Y, and major influence factors X=[x1,x2,...,xn]；
2) sophisticated testing influence factor x, is obtainediProbability density function gxi(ξi), ξiFor the measured value of influence factor；
3), using probability density function gx of the Latin Hypercube Sampling method according to influence factori(ξi) test sampling is carried out, obtain
To the experimental design table D of influence factorn, tested according to the parameter of design table, obtain sophisticated testing under each input parameter
As a result Yi；
4), the uncertainty of sophisticated testing is evaluated based on Bayes principle：
4.1) with step 3) result of the test YiPartial data as priori sample, another part is used as current measurement sample；
4.2) mean μ of priori sample is calculated0With the standard deviation τ of average, and current measurement sample averageWith standard deviation s；
4.3) estimation of measured true value is calculated using shown formula
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Wherein n is current measurement total sample number；
4.4) standard uncertainty σ is calculated using shown formula
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4.5) by the estimation of obtained measured true valueIt is corresponding with standard uncertainty σ calculating to include interval comprising Probability p
[ylow,yhigh], wherein ylowAnd yhighIt is respectively minimum value and maximum in interval to calculate；
5) step 4.4, is exported) and 4.5) result is used as uncertainty evaluation.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109063233A (en) * | 2018-06-15 | 2018-12-21 | 中国核电工程有限公司 | It is a kind of to evaluate radionuclide content to k with Monte Carlo methodeffThe method that uncertainty influences |
| CN111339497A (en) * | 2020-03-05 | 2020-06-26 | 南京工业大学 | Probability prediction model for evaluating strength index of recycled concrete |
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| CN103049639A (en) * | 2012-10-30 | 2013-04-17 | 中国电子科技集团公司第十三研究所 | Noise parameter measurement uncertainty evaluation method based on multi-chip module (MCM) |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109063233A (en) * | 2018-06-15 | 2018-12-21 | 中国核电工程有限公司 | It is a kind of to evaluate radionuclide content to k with Monte Carlo methodeffThe method that uncertainty influences |
| CN111339497A (en) * | 2020-03-05 | 2020-06-26 | 南京工业大学 | Probability prediction model for evaluating strength index of recycled concrete |
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Application publication date: 20170901 |