CN106779081B - A kind of carrier rocket fifth wheel estimating method based on bayesian theory - Google Patents
A kind of carrier rocket fifth wheel estimating method based on bayesian theory Download PDFInfo
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Abstract
The invention discloses a kind of carrier rocket fifth wheel estimating method based on bayesian theory, comprising the following steps: (1) establish fifth wheel model, and sample；(2) by the fifth wheel model simplification at black box taking ball model；(3) it is based on the black box taking ball model, calculate all probable values of black ball number, and the probability of each probable value is calculated according to Bayes' theorem, probability distributing density function of the probability distributing density function of black ball as fifth wheel quantity is obtained, and draws curve graph using the corresponding probability of the probable value of the probable value of black ball number as abscissa, black ball number as ordinate；(4) according to the probability distributing density function of fifth wheel quantity, the value interval of the fifth wheel quantity under the inferred value of final fifth wheel quantity, and setting confidence level is calculated.Compared with prior art, the present invention is more reasonable, accurate.
Description
Technical field
The present invention relates to a kind of carrier rocket fifth wheel estimating method more particularly to a kind of deliveries based on bayesian theory
Rocket fifth wheel estimating method.
Background technique
The success or failure of fifth wheel control planning space flight the model such as carrier rocket, satellite of fuel tank and oxidizer tank, to its into
The control of row fifth wheel is the important work of development process.Tank fifth wheel mainly includes cutting, powder, burr, welding slag etc., is checked
Method for cleaning includes the outside that bay section is gently beaten with film hammer, and slight shaking is carried out to bay section, viscous net small with white glue cloth
Clast etc.；Also there are the various advanced means such as ultrasonic wave, endoscope to extra object detecting method；Meanwhile passing through technique, process, system
Degree etc. carries out strict control, but under conditions present, the appearance of fifth wheel is that development process is inevitable, extra in order to carry out
Object control, it is therefore desirable to which statistical inference is carried out to the quantity of fifth wheel.
In space flight model, common method is exactly proportionally to be inferred, there is a problem with large errors；In classics
In statistical method, to problems frequently with the statistical inference of bi-distribution, but fifth wheel quantity survey and bi-distribution area
Between or different from, fifth wheel quantity survey is related with the area ratio of inspection, i.e., inspection area mostly than check area it is few
More credible, the interval estimation of bi-distribution can not embody this property.For example, 100% inspection is carried out to fifth wheel quantity,
Confidence level reaches 1, dramatically different with the calculated result of bi-distribution.Its reason first is that bi-distribution consider population sample without
Limit, but fifth wheel quantity is limited.
Currently used statistical analysis technique often assumes that its probability distribution, or is fitted to obtain its probability by data
Distribution, carries out statistical inference on the basis of probability distribution.But for fifth wheel, without specific probability distribution mould
Type, also without a large amount of statistical data.So, it is assumed that the method for inspection is not very suitable to the deduction of fifth wheel quantity yet.
Currently, having urgent actual demand to fifth wheel quantity survey, lack more reasonable accurately fifth wheel number at present
Measure estimating method.
Summary of the invention
It is of the invention a kind of more rationally accurately to be managed based on Bayes in view of the above-mentioned problems of the prior art, providing
The carrier rocket fifth wheel estimating method of opinion.
In order to solve the above technical problems, the present invention is achieved through the following technical solutions: a kind of based on bayesian theory
Carrier rocket fifth wheel estimating method, comprising the following steps:
(1) divided by space and quantified, establish fifth wheel model, and sample；
(2) by the fifth wheel model simplification at black box taking ball model；
(3) it is based on the black box taking ball model, calculates all probable values of black ball number, and is calculated according to Bayes' theorem
The probability of each probable value out obtains probability distribution density letter of the probability distributing density function as fifth wheel quantity of black ball
Number, and song is drawn using the corresponding probability of the probable value of the probable value of black ball number as abscissa, black ball number as ordinate
Line chart；
(4) according to the probability distributing density function of fifth wheel quantity, the inferred value of final fifth wheel quantity, Yi Jishe are calculated
Determine the value interval of the fifth wheel quantity under confidence level.
The step (1) specifically: the total space of carrier rocket is divided into mutually disjoint N number of space cell, and
K space cell is surveyed sample, there are T to contain fifth wheel in the K space cell.
The step (2) specifically: indicate N number of space cell with N number of ball, extract K ball to indicate K space
Unit, black ball have T to indicate having T is a to contain fifth wheel in the K space cell, indicate not no fifth wheel with Archon
Space cell.
The step (3) specifically:
(31) all probable value x of black ball number are calculatedi,
Wherein, i is integer；
(32) K ball is extracted again, under conditions of wherein black ball has i, calculates and extracts K ball, and wherein black ball has a general of T
Rate p (B | Ai),
Wherein, i=T, T+1 ... N-K+T, i are integer；
(33) probability of each non-zero probable value of black ball is calculated, then extracts K ball, wherein black ball there are T conditions
Under, it calculates and extracts K ball, wherein black ball has i Probability psi,
Wherein, i=T, T+1 ... N-K+T, i are integer；
(34) according to pi, the probability density function i.e. probability density function of fifth wheel of black ball is obtained, and with black ball number
Probable value be abscissa, black ball number the corresponding probability of probable value be ordinate draw curve graph.
The step (4) specifically: as most after being rounded the value of the corresponding abscissa in highest point in the curve graph
Then the inferred value of whole fifth wheel quantity according to the credibility interval calculation method in Bayes' theorem, calculates under setting confidence level
Credibility interval and value interval as fifth wheel quantity.
Compared with prior art, the present invention is built for the feature that carrier rocket fifth wheel total amount is unknown, distribution characteristics is unknown
Corresponding mathematical model is found, according to Bayes' theorem, the probability density function of fifth wheel quantity is given, is given by sampling sample
The method that this information inference goes out the information of sample totality, and overall probability density function is given, the present invention is rationally accurate, more
It is practical to stick on conjunction, avoids the deficiency of conventional method, currently without the explanation or report for finding technology similar to the present invention, also still
It is not collected into data similar both at home and abroad.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the probability density distribution of the fifth wheel quantity acquired in the embodiment of the present invention.
Specific embodiment
It elaborates below to the embodiment of the present invention, the present embodiment carries out under the premise of the technical scheme of the present invention
Implement, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to following implementation
Example.
The following property of Bayes' theorem-sampling and overall relation:
(1) in the case that sample is overall centainly, sampling samples number is more, and under same confidence level, credibility interval is got over
It is small；
(2) identical sampling samples ratio, sample totality number is bigger, and credibility interval is smaller (same confidence level)；
(3) identical sampling number, different samples is overall, and the probability distributing density function PMF of fifth wheel ratio is identical.
Using this method, following assessment can be carried out:
(1) according to single sample situation, the probability distributing density function PMF of sample totality is obtained, it is close using probability distribution
Function PMF is spent, under given confidence level, calculates overall credibility interval；
(2) probability distributing density function PMF is utilized, is required according to confidence level and credibility interval requires, design sampling side
Case, i.e. single sample sample size.
As shown in Figure 1, a kind of carrier rocket fifth wheel estimating method based on bayesian theory, comprising the following steps:
(1) total space of carrier rocket is divided into mutually disjoint N number of space cell, and surveys sample K space
Unit has in K space cell T to contain fifth wheel, the size of fifth wheel can be set as the size of space cell, extra
There are certain ranges to choose size of the big fifth wheel size as space cell for conservative estimation for the size of object；
(2) it indicates N number of with N number of ball and is extracting space cell, extract K ball to indicate that K space cell, black ball have T
It is a to indicate to have in K space cell T to contain fifth wheel, the space cell of not fifth wheel is indicated with Archon；Distinguishingly,
But relatively common situation is in engineering: N number of ball altogether, extracts K, and discovery is all Archon, i.e. black ball number T is 0.By this
The transformation of model, can the rough sample global restriction statistics in an approximate range, because of the ruler of fifth wheel individual
Very little size has an approximate range essentially according to experience.
(3) it is based on black box taking ball model, calculates all probable values of black ball number, and is calculated often according to Bayes' theorem
A kind of probability of probable value obtains probability distributing density function of the probability distributing density function of black ball as fifth wheel quantity,
And curve is drawn using the corresponding probability of the probable value of the probable value of black ball number as abscissa, black ball number as ordinate
Figure；Specific steps are as follows: (31) calculate all probable value x of black ball numberi,
Wherein, i is integer；
(32) K ball is extracted again, under conditions of wherein black ball has i, calculates and extracts K ball, and wherein black ball has a general of T
Rate p (B | Ai),
Wherein, i=T, T+1 ... N-K+T, i are integer；
(33) probability of each non-zero probable value of black ball is calculated, then extracts K ball, wherein black ball there are T conditions
Under, it calculates and extracts K ball, wherein black ball has i Probability psi,
Wherein, i=T, T+1 ... N-K+T, i are integer；
(34) according to pi, the probability density function i.e. probability density function of fifth wheel of black ball is obtained, and with black ball number
Probable value be abscissa, black ball number the corresponding probability of probable value be ordinate draw curve graph.
(4) deduction after being rounded the value of the corresponding abscissa in highest point in curve graph as final fifth wheel quantity
Then value according to the credibility interval calculation method in Bayes' theorem, calculates the credibility interval under setting confidence level and as more
The value interval of excess quantity.Specifically, confidence level γ is set, credibility interval is [pγ,p1-γ], unilateral confidence upper limit: pγ=
pH, unilateral confidence lower limit: pγ=pL, wherein pLMeet
It is a kind of undesirable state since black ball indicates fifth wheel, it is the smaller the better, therefore select confidence upper limit.
There are two features for the presence tool of fifth wheel: first is that total amount is unknown, second is that distribution characteristics is unknown.Known information is inspection
It include the space cell number of fifth wheel in the space cell of space cell number, total space unit number and the inspection looked into.
The tank situation of the present embodiment is as follows:
In the present embodiment, N=430, K=43, T=0.Probability density function curve graph such as Fig. 2 institute that the present embodiment obtains
Show.According to probability density function, it is 0 that fifth wheel quantity inferred value, which is calculated, in the case where confidence level is 0.9, fifth wheel
Up to 20；In the case where confidence level is 0.7, fifth wheel is up to 14.
Claims (5)
1. a kind of carrier rocket fifth wheel estimating method based on bayesian theory, which comprises the following steps:
(1) fifth wheel model is established, and is sampled；
(2) by the fifth wheel model simplification at black box taking ball model；
(3) it is based on the black box taking ball model, calculates all probable values of black ball number, and is calculated often according to Bayes' theorem
A kind of probability of probable value obtains probability distributing density function of the probability distributing density function of black ball as fifth wheel quantity,
And curve is drawn using the corresponding probability of the probable value of the probable value of black ball number as abscissa, black ball number as ordinate
Figure；
(4) according to the probability distributing density function of fifth wheel quantity, the inferred value of final fifth wheel quantity is calculated, and setting can
The value interval of fifth wheel quantity under reliability.
2. a kind of carrier rocket fifth wheel estimating method based on bayesian theory as described in claim 1, which is characterized in that
The step (1) specifically: the total space of carrier rocket is divided into mutually disjoint N number of space cell, and surveys sample K
A space cell has in the K space cell T to contain fifth wheel.
3. a kind of carrier rocket fifth wheel estimating method based on bayesian theory as claimed in claim 2, which is characterized in that
The step (2) specifically: indicate that N number of space cell, K ball of extraction are black to indicate K space cell with N number of ball
Ball has T to indicate having T to contain fifth wheel in the K space cell, indicates that the space of not fifth wheel is single with Archon
Member.
4. a kind of carrier rocket fifth wheel estimating method based on bayesian theory as claimed in claim 2, which is characterized in that
The step (3) specifically:
(31) all probable value x of black ball number are calculatedi,
Wherein, i is integer；
(32) K ball is extracted again, under conditions of wherein black ball there are i, is calculated and is extracted K ball, wherein black ball there are T Probability ps
(B|Ai),
Wherein, i=T, T+1 ... N-K+T, i are integer；
(33) probability of each non-zero probable value of black ball is calculated, then extracts K ball, under conditions of wherein black ball has T, meter
It calculates and extracts K ball, wherein black ball has i Probability psi,
Wherein, i=T, T+1 ... N-K+T, i are integer；
(34) according to pi, the probability density function i.e. probability density function of fifth wheel of black ball is obtained, and with the possibility of black ball number
Value be abscissa, black ball number the corresponding probability of probable value be ordinate draw curve graph.
5. a kind of carrier rocket fifth wheel estimating method based on bayesian theory as described in claim 1, which is characterized in that
The step (4) specifically: final fifth wheel is used as after being rounded the value of the corresponding abscissa in highest point in the curve graph
Then the inferred value of quantity according to the credibility interval calculation method in Bayes' theorem, calculates the confidence region under setting confidence level
Between and the value interval as fifth wheel quantity.
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Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101710368A (en) * | 2009-12-21 | 2010-05-19 | 北京航空航天大学 | Bayesian reliability comprehensive estimation method based on multisource degraded data |
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| US8655821B2 (en) * | 2009-02-04 | 2014-02-18 | Konstantinos (Constantin) F. Aliferis | Local causal and Markov blanket induction method for causal discovery and feature selection from data |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101710368A (en) * | 2009-12-21 | 2010-05-19 | 北京航空航天大学 | Bayesian reliability comprehensive estimation method based on multisource degraded data |
Non-Patent Citations (3)
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| "基于知识的贝叶斯诊断网络模型建造方法";周海刚 等;《飞机设计》;20090430;第29卷(第2期);第41-45页 |
| "条件概率中三个公式的应用";刘修生;《黄石高等专科学校学报》;20040430;第20卷(第2期);第50-52页 |
| "贝叶斯分类器在液体火箭发动机";李京浩 等;《火箭推进》;20071231;第33卷(第6期);第13-16页 |
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