CN110516288A - It is a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use - Google Patents
It is a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use Download PDFInfo
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Abstract
The invention discloses a kind of to using relevant aero-engine loading spectrum Mixture Distribution Model method for building up, divides firstly, the normal g-load and rotation spectrum to all flight mission profiles carry out section of taking off, interlude, landing section.The interlude of all sections and all maneuver classes sections is spliced, splicing spectrum is obtained and is composed with the splicing of maneuver classes interlude.It is for statistical analysis to all sections splicing spectrum again, and detected by thick tail and determine that normal g-load has thick tail characteristic.Secondly, corresponding normal g-load coefficient value is extracted in maneuver classes interlude splicing spectrum at 100% revolving speed as threshold data library, takes the threshold value of frequency of occurrence is most in threshold data library normal g-load coefficient value as the type aero-engine normal g-load coefficient Mixture Distribution Model.Finally, the normal g-load coefficient for being greater than threshold value in all sections splicing spectrum is defined as Extreme Load Distributions, middle low load will be defined as lower than the normal g-load coefficient of threshold value in all sections splicing spectrum, obtain in low, Extreme Load Distributions mixed distributions.
Description
Technical field
It is the invention belongs to aero-engine loading spectrum data statistics technical field, in particular to a kind of with the relevant boat of use
Empty engine load composes Mixture Distribution Model method for building up.
Background technique
The load that aeroengine components are born in practical flight is continuously to change at random, an aerial mission
Load-time graph be aero-engine loading spectrum.Engine load spectrum has recorded aero-engine in actual use
Pneumatic, hot, mechanical load the ratio and size born, major parameter have flying height, engine speed, turbine after-burning
Temperature degree or engine power control arm angle etc..Loading spectrum is through in engine health evaluation and actually using, so starting
During machine designs, tests and determine the longevity, loading spectrum all plays an important role.
The parameters such as height, speed, revolving speed and normal g-load coefficient in engine load spectrum can directly determine aeroplane engine
Loaded-up condition in machine practical flight.And normal g-load has direct shadow for the aero-engines component such as casing and turbine wheel shaft
It rings.So research is sent to the accurate statistics of overload factor spectrum and is distributed the design to aero-engine and determines the service life with important meaning
Justice.Regulation in aero-engine structural intergrity guide (GJB/Z101-1997), normal g-load Extreme Load Distributions are aero-engines
Structural reliability design important parameter and aero-engine sizing take a flight test and need the content examined.Determine that the extreme value of normal g-load carries
Lotus distribution has very important meaning to the safe operation of engine.
Due to technology blockage, the pertinent literature of foreign study normal g-load Extreme Load Distributions distribution is difficult to consult, and domestic pass
Also less in the document of research normal g-load Extreme Load Distributions distribution, document " utilizes III forecast of distribution aircraft normal direction of Pearson-
Overload extreme value " Extreme Load Distributions for studying in ([J] mechanical strength, 2018 (1)) are peak load in normal g-load spectrum, and
III distribution probability density function expression formula of Pearson- is more many and diverse, and practical application is difficult.Other documents compose overload factor
The distribution of Extreme Load Distributions is to be analyzed based on statistics data, and the selection of threshold value is even more to depend on research people mostly
The experience and knowledge of member is horizontal, subjective.
Normal g-load coefficient spectrum can intuitively show the variation of aero-engine maneuver, and the present invention is with normal direction mistake
Carrying coefficient spectrum is object expansion research.And normal g-load Extreme Load Distributions have for the safe operation of aero-engine it is particularly important
Influence, urgent need is established a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model of use, carrys out accurate judgement normal direction mistake
Carry load distribution.Thus, it is necessary to which it is determining to establish a kind of normal g-load polarographic maximum load distribution threshold value relevant to actual use
Method.
Summary of the invention
The present invention proposes one kind and the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use.This method
The distribution that can accurately determine Extreme Load Distributions effectively calculates Extreme Load Distributions that may be present in the entire lifetime of engine.In
Guarantee in turn avoid surdimensionnement while safe design, to later loading spectrum establishment, stress analysis, life prediction etc.
It is of great significance.
To achieve the above object, the technical solution adopted by the present invention are as follows:
It is a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use, comprising the following steps:
(1) the actual measurement normal direction overload factors of several sections of aero-engine spectrum is gone to be divided into rotating speed spectrum take off,
All sections and maneuver classes interlude are carried out ending splicing by intermediate, landing section, obtain all sections splicing spectrums of normal g-load with
Maneuver classes interlude splicing spectrum；
(2) spectrum is spliced to all sections and carries out frequency statistics, the distribution characteristics of tail data is obtained to analysis of statistical results,
Spectrum is spliced to normal g-load coefficient again and carries out thick tail detection, determines its distribution, and establish corresponding Mixture Distribution Model；
(3) flight revolving speed splicing spectrum and normal g-load coefficient splicing spectrum are combined, maneuver classes interlude splicing spectrum 100% is extracted
Corresponding normal g-load coefficient value is as threshold data library at revolving speed；Take the normal g-load that frequency of occurrence is most in threshold data library
Threshold value of the coefficient value as the type aero-engine normal g-load coefficient Mixture Distribution Model；
(4) the normal g-load coefficient for being greater than threshold value in all sections splicing spectrum is defined as Extreme Load Distributions, less than threshold value
Normal g-load coefficient is defined as middle low load, obtain in low, Extreme Load Distributions mixed distributions.
Further, step (1) specific steps are as follows:
(11) research object be normal g-load spectrum loading distribution, flight mission profile according to actual use be divided into maneuver classes with
Course line class, the revolving speed and normal g-load of maneuver classes mission profile are composed, and rotation speed change feature is that interlude has more revolving speed acute
Strong variation, corresponding normal g-load load characteristic are that interlude has more Extreme Load Distributions variation, and course line generic task section turns
Speed is composed with normal g-load, and the feature of rotation speed change is smaller for interlude rotation speed change, and corresponding normal g-load load characteristic
Also it is little to show as load change amplitude, and normal g-load coefficient is all smaller, but the section of taking off of both types mission profile and
The feature that landing section is shown is with uniformity, i.e. normal g-load coefficient is all less than normal；
(12) flight mission profile is divided into three sections, is followed successively by section of taking off, interlude and section of landing, and stroke of task segment
Divide and need engine speed spectrum, normal g-load spectrum comparing division jointly, section of taking off is defined as starting from scratch when revolving speed
After reaching maximum (top) speed, when revolving speed drops to steady state value, it is believed that section of taking off terminates；When revolving speed is begun to decline and is not returned to
Maximum (top) speed, and gradually decrease to zero, it is believed that this section is landing section；Remainder is interlude；As shown in Figure 4.Such stroke
The normal g-load spectrum that effectively removed of point method is taken off the small overload factor of section of landing, and aero-engine actual use feelings are met
Condition, so choosing such division methods；
(13) all sections are spliced, obtains all section splicing spectrums；As shown in figure 4, section of taking off and landing section portion
Divide normal g-load less than normal, the distribution of normal g-load Extreme Load Distributions is not influenced, section of taking off and landing section removal go several
Except the revolving speed and normal g-load spectrum of the maneuver classes mission profile of section of taking off and landing section carry out head and the tail splicing, obtain among maneuver classes
Section splicing spectrum.
Further, in the step (12), section of taking off revolving speed drops to steady state value, and the steady state value is maximum (top) speed
5%.
Further, step (2) specific steps are as follows:
(21) all section normal direction overload factor splicing spectrums obtained in step (1) are for statistical analysis, it obtains
To frequency statistics figure, as shown in Figure 6.It can be seen from the figure that aero-engine interlude load data is in intermediate several sections
Inside show high concentration, and the distribution of Extreme Load Distributions part is more dispersed, the distribution of tail data fractional load the frequency with
The increase of load and reduce, but reduce that amplitude is slow, and such Distribution Phenomena is similar to probability statistics " thick tail point
Cloth ".To determine if to have thick tail characteristic, need to carry out sample data thick tail detection, thick tail detection main method has Q-Q
Figure method (quantile-quantile plot) and trailing pole value index number method.Both methods is passed different judgements on, so we use two
Kind method carries out thick tail detection to sample data, to ensure that tail data meets " thick tail distribution "；
(22) sample data known to step (21) meets thick tail distribution, to three kinds of classical Extreme Load Distributions distribution theorys
(district's groups maximum model (Block Maxima Method), independent storm model (Method of Independent
Storms), superthreshold model (Peak Over Threshold)) it compares.Wherein, district's groups maximum model is only chosen on a small quantity
Extreme Load Distributions cause data waste, can not represent the distribution situation of Extreme Load Distributions as sample data；Independent storm model
It is larger to sample data required amount, unstable, engineer application difficulty is estimated for extreme value；Superthreshold model can make full use of extreme value
Load data, practical application is also relatively simple, so this model being most widely used on engineer application.
Based on the above comparison, superthreshold model (abbreviation POT) Lai Jianli aero-engine normal g-load coefficient spectrum is used herein
Mixture Distribution Model.Then the Mixture Distribution Model of aero-engine normal g-load coefficient spectrum is established using superthreshold model,
Assuming that sum is the normal g-load x of ni: x1,x2,…,xi,…,xn(1≤i≤n) is independent identically distributed random change
Sample is measured, overall distribution function F (x is obeyedi) mathematical distribution, u is an abundant big threshold value, and load value is more than threshold value in sample
The number of samples of u is Nu；If xi> u, then claim xiFor superthreshold, y=xi- u be plussage, claim plussage be distributed as condition beyond point
Cloth function Fu(y):
Wherein: P (xi-u≤y|xi> u) it is xiWhen > u, xiThe conditional probability of≤y+u；
That is:
The overall distribution function for indicating sample beyond distribution function with condition, indicates are as follows:
F(xi1-F)=[(u)] × Fu(y)+F(u) (12)
Wherein, xi>u,0≤y≤xi-u；
If overall distribution function F (x) be it is known, pole can be described by the distribution of superthreshold and the distribution of plussage
It is worth sample.However, engineering actual use in, F (x) be usually it is unknown, therefore, to the Limit Distribution of plussage and superthreshold
Research is just particularly important.
Further, the thick tail detection method has Q-Q figure method (quantile-quantile plot) to refer to trailing pole value
Number method.
Further, the physical significance of the Q-Q figure method are as follows: if the distribution for the data being independently distributed divides close to normal state
Cloth, then the scatterplot in Q-Q figure should approximate straight line；If Q-Q figure scatterplot has convex trend, show that the quantile of data increases
Long speed is faster than normal distribution, this sample data tail portion has thick tail characteristic.
Further, the specific steps of the Q-Q figure method are as follows:
(a) sum is set as the normal g-load x of ni:x1,x2,…,xi,…,xn(1≤i≤n) meets normal distribution, quantile
qiAre as follows:
Wherein, pi=(i-1/2)/n is xi≤qiProbability；I=1,2 ..., n is i-th of element of sample；E is nature
Constant；π is pi；
(b) sample data is arranged from small to large, is obtained: x11,x12,…,x1n, corresponding probability value is p1=(1-
1/2)/n,p2=(2-1/2)/n ..., pn=(n-1/2)/n；Corresponding normal state quantile q is calculated according to formula (4)1,
q2,…,qn, by several to (qi,x1i), (i=1,2 ... n) depict on a coordinate plane, and sample fractiles are increasing ratio just
State distribution is fast, and apparent convex trend is presented in sample fractiles number curve, then the sample data has thick tail characteristic.
Further, the specific steps of the trailing pole value index number method are as follows:
If the normal g-load that sum is n is xi:x1,x2,…,xi,…,xn(1≤i≤n), in which: i is i-th in ordered series of numbers
Element；Sample data is arranged from small to large and is obtained: x11,x12,…,x1n, then, the Monent type estimator of sampleExpression
Formula are as follows:
Wherein, trailing pole coefficient
Trailing pole coefficientThe value of trailing pole parameter m is determined according to n, takes m=n/
It 10 and is rounded, ifThen sample belongs to thin tail distribution；IfThen sample meets thick tail distribution.
Further, step (3) specific steps are as follows:
No matter which kind of Extreme Load Distributions distributed model selected, the selection of threshold value is all important one of step.The present invention is root
It actually uses and chooses according to aero-engine, have more physical significance.Rotating speed spectrum and overload spectrum are all reflection engine actual uses
Situation, such as Fig. 5 it can be seen that while with rotation speed change, normal g-load spectrum also changes therewith.So normal g-load
The Extreme Load Distributions of spectrum and the maximum (top) speed of rotating speed spectrum have certain synchronism.
The related coefficient of rotating speed spectrum and normal g-load spectrum is obtained by calculation, the two reaches highly relevant, then turns maximum
The corresponding normal g-load coefficient of speed extracts, as threshold data library undetermined；The data in threshold data library undetermined are carried out general
Rate statistics, corresponds to the highest normal g-load coefficient of the frequency of occurrences as threshold value when using maximum (top) speed.By threshold data library undetermined
Data carry out probability statistics, are reasonable as threshold value using the highest normal g-load coefficient of probability and meet real engine reality
Service condition.
Further, in the step (3), related coefficient, which calculates, uses the related coefficient calculation method based on rain flow way,
Related coefficient is the index of degree of correlation between measuring multi-parameter, is indicated with alphabetical r, value is between -1~1, related coefficient
Not equidistant metric, an alphabetic data, calculate related coefficient when, need biggish sample size, can just obtain compared with
It generallys use for reliable related coefficient numerical value in mathematical statistics to calculate the related coefficient of two groups of sample datas.Calculate two
When the related coefficient of group sample, it is necessary to assure the sample size of two groups of data is identical, normal g-load xiWith revolving speed yiCoefficient of relationship r
Are as follows:
In formula,Average is overloaded for discovery,For revolving speed average.
Further, step (4) specific steps are as follows:
It for middle low load, chooses Two-parameter Weibull Distribution and is fitted, there is thick tail characteristic for Extreme Load Distributions, adopt
With having the mathematical distribution of thick tail characteristic to be fitted it, low load obeys the generalized extreme value point with thick tail characteristic in setting
Cloth (GEV), therefore, overall distribution function is mixed by Two-parameter Weibull Distribution and generalized extreme value distribution, mixed distribution
Function Fmix(x) are as follows:
Wherein, Fw(x, η, β) is Two-parameter Weibull Distribution, and η is scale parameter；β is in Two-parameter Weibull Distribution
Form parameter (η > 0, β > 0)；FGEV(x, u, σ, ξ) is generalized extreme value distribution, and ξ is the form parameter in generalized extreme value distribution；μ is
Location parameter；σ is dimensional parameters；U is threshold value；X is the element in all sections splicing spectrum.
Two-parameter Weibull Distribution cumulative distribution function fw(x) are as follows:
Generalized extreme value cumulative distribution function fGEV(x) are as follows:
Compared with prior art, the invention has the following advantages:
Present invention employs statistics to actually use the thought combined with aero-engine, to rotating speed spectrum and normal g-load
Spectrum compares selected threshold, compared with existing aero-engine Model of extreme distribution, has following significant advantage:
(1) there is specific practical significance；This model is determined by the high correlation that rotating speed spectrum is composed with normal g-load
Threshold value.It is more reasonable by experience selected threshold choosing method relative to other models, therefore more practical significance.
(2) there is stronger versatility；This model using simple, Research on threshold selection for other Model of extreme distribution all
It is applicable in, there is stronger versatility.
(3) with extensive engineering application value: the threshold value in loading spectrum statistics field is chosen the reality with aero-engine
Border behaviour in service combines.Guarantee point that can accurately obtain Extreme Load Distributions and middle low load while data are fully used again
Cloth situation, engineering application value are more extensive.
(4) present invention loading spectrum establishment later to aero-engine, stress analysis, life prediction etc. has important
Meaning.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is that the revolving speed of typical motor generic task section and normal g-load are composed；
Fig. 3 is that the revolving speed of typical course line generic task section and normal g-load are composed；
Fig. 4 be take off, the division for section of landing
Fig. 5 is normal g-load coefficient and motor-driven rotating speed spectrum constitutional diagram (segment)；
Fig. 6 is normal g-load coefficient spectrum frequency statistics figure；
Fig. 7 is sample Q-Q figure；
Fig. 8 is the corresponding normal g-load coefficient (segment) of 100% revolving speed of maneuver classes rotating speed spectrum or more；
Fig. 9 is the corresponding normal g-load coefficient probability statistics figure of 100% revolving speed of maneuver classes rotating speed spectrum or more；
Figure 10 is less than the normal g-load coefficient data statistical chart of threshold value；
Figure 11 is low load data cumulative probability curve in Two-parameter Weibull Distribution fitting；
Figure 12 is above the normal g-load coefficient data statistical chart of threshold value；
Figure 13 is generalized extreme value distribution fitting Extreme Load Distributions data cumulative probability curve.
Specific embodiment
Below with reference to embodiment, the present invention will be further explained.
The present invention selects normal direction overload factor spectrum as research object, true by corresponding engine speed polarographic maximum
The threshold value for determining overload factor spectrum finally obtains the distribution of overload factor spectrum loading.
Embodiment 1
It is a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use, with certain type aero-engine
For normal g-load coefficient, Planning procedure figure is as shown in Figure 1, comprising the following steps:
(1) the actual measurement normal direction overload factors of several sections of aero-engine spectrum is gone to be divided into rotating speed spectrum take off,
All sections and maneuver classes interlude are carried out ending splicing by intermediate, landing section, obtain all sections splicing spectrums of normal g-load with
Maneuver classes interlude splicing spectrum；
Step (1) specific steps are as follows:
(11) research object be normal g-load spectrum loading distribution, flight mission profile according to actual use be divided into maneuver classes with
Course line class, the revolving speed and normal g-load of maneuver classes mission profile are composed, and rotation speed change feature is that interlude has more revolving speed acute
Strong variation, corresponding normal g-load load characteristic are that interlude has more Extreme Load Distributions variation, and course line generic task section turns
Speed is composed with normal g-load, and the feature of rotation speed change is smaller for interlude rotation speed change, and corresponding normal g-load load characteristic
Also it is little to show as load change amplitude, and normal g-load coefficient is all smaller, but the section of taking off of both types mission profile and
The feature that landing section is shown is with uniformity, i.e. normal g-load coefficient is all less than normal；
(12) flight mission profile is divided into three sections, is followed successively by section of taking off, interlude and section of landing, and stroke of task segment
Divide and need engine speed spectrum, normal g-load spectrum comparing division jointly, section of taking off is defined as starting from scratch when revolving speed
After reaching maximum (top) speed, when revolving speed drops to steady state value (the 5% of maximum (top) speed), it is believed that section of taking off terminates；When revolving speed is opened
Begin to decline and do not return to maximum (top) speed, and gradually decrease to zero, it is believed that this section is landing section；Remainder is interlude；
As shown in Figure 4.The normal g-load spectrum that effectively removed of such division methods is taken off the small overload factor of section of landing, and aviation hair is met
Motivation actually uses situation, so choosing such division methods；
(13) research object of the present invention is the distribution of normal g-load spectrum loading.Generality rule in order to obtain, reply is as far as possible
More normal g-load spectrums is for statistical analysis.All section head and the tail are spliced, whole section splicing spectrums are obtained.Flight mission profile
Maneuver classes and two kinds of course line class can be divided into according to actual use.The revolving speed and normal g-load of typical motor generic task section are composed,
Rotation speed change feature is that interlude has more revolving speed acute variation, and corresponding normal g-load load characteristic has more for interlude
Extreme Load Distributions variation, as shown in Figure 2.The revolving speed and normal g-load of typical course line generic task section are composed, the spy of rotation speed change
Sign is that interlude rotation speed change is smaller, and also to show as load change amplitude little for corresponding normal g-load load characteristic, and method
It is all smaller to overload factor, as shown in Figure 3.But the feature that the rear and front end of both types mission profile is shown has one
Cause property, i.e. normal g-load coefficient is all less than normal.Section of taking off as shown in Figure 4 and landing section part normal g-load are less than normal, to normal g-load
Extreme Load Distributions distribution has little effect, can be first by section of taking off and landing section removal to reduce calculation amount.It is finally that institute is organic
The interlude head and the tail of dynamic class section splice, and it is as shown in Figure 5 to obtain splicing spectrum among motorized segment.
All sections are spliced, all section splicing spectrums are obtained；As shown in figure 4, section of taking off and landing section part method
It is less than normal to overloading, the distribution of normal g-load Extreme Load Distributions is not influenced, section of taking off and landing section removal remove several
The revolving speed and normal g-load spectrum for flying the maneuver classes mission profile of section and section of landing carry out head and the tail splicing, obtain the spelling of maneuver classes interlude
Connect spectrum.
(2) spectrum is spliced to all sections and carries out frequency statistics, the distribution characteristics of tail data is obtained to analysis of statistical results,
Spectrum is spliced to normal g-load coefficient again and carries out thick tail detection, determines its distribution, and establish corresponding Mixture Distribution Model；
Step (2) specific steps are as follows:
(21) all section normal direction overload factor splicing spectrums obtained in step (1) are for statistical analysis, it obtains
To frequency statistics figure, as shown in Figure 6.It can be seen from the figure that aero-engine interlude load data is in intermediate several sections
Inside show high concentration, and the distribution of Extreme Load Distributions part is more dispersed, the distribution of tail data fractional load the frequency with
The increase of load and reduce, but reduce that amplitude is slow, and such Distribution Phenomena is similar to probability statistics " thick tail point
Cloth ".To determine if to have thick tail characteristic, need to carry out sample data thick tail detection, thick tail detection main method has Q-Q
Figure method (quantile-quantile plot) and trailing pole value index number method.Both methods is passed different judgements on, so we use two
Kind method carries out thick tail detection to sample data, to ensure that tail data meets " thick tail distribution "；
Further, the thick tail detection method has Q-Q figure method (quantile-quantile plot) to refer to trailing pole value
Number method.
Further, the physical significance of the Q-Q figure method are as follows: if the distribution for the data being independently distributed divides close to normal state
Cloth, then the scatterplot in Q-Q figure should approximate straight line；If Q-Q figure scatterplot has convex trend, show that the quantile of data increases
Long speed is faster than normal distribution, this sample data tail portion has thick tail characteristic.
Further, the specific steps of the Q-Q figure method are as follows:
(a) sum is set as the normal g-load x of ni:x1,x2,…,xi,…,xn(1≤i≤n) meets normal distribution, quantile
qiAre as follows:
Wherein, pi=(i-1/2)/n is xi≤qiProbability；I=1,2 ..., n is i-th of element of sample；E is nature
Constant；π is pi；
(b) sample data is arranged from small to large, is obtained: x11,x12,…,x1n, corresponding probability value is p1=(1-
1/2)/n,p2=(2-1/2)/n ..., pn=(n-1/2)/n；Corresponding normal state quantile q is calculated according to formula (4)1,
q2,…,qn, by several to (qi,x1i), (i=1,2 ... n) depict on a coordinate plane, and sample fractiles are increasing ratio just
State distribution is fast, and apparent convex trend is presented in sample fractiles number curve, then the sample data has thick tail characteristic.
According to method as above, obtains Q-Q figure and be illustrated in fig. 7 shown below.The physical significance of Q-Q figure method are as follows: if the number being independently distributed
According to distribution is close and normal distribution, then the scatterplot in Q-Q figure should approximate straight line；If Q-Q figure scatterplot has convex trend,
Then show that the quantile growth rate of data is faster than normal distribution, this sample data tail portion has thick tail characteristic.It can be seen that
Extreme Load Distributions sample fractiles increase, sample fractiles number curve presentation apparent convex trend, so tail portion faster than normal distribution
Data have thick tail characteristic.
Further, the specific steps of the trailing pole value index number method are as follows:
If the normal g-load that sum is n is xi:x1,x2,…,xi,…,xn(1≤i≤n), in which: i is i-th in ordered series of numbers
Element；Sample data is arranged from small to large and is obtained: x11,x12,…,x1n, then, the Monent type estimator of sampleExpression
Formula are as follows:
Wherein, trailing pole coefficient
Trailing pole coefficientThe value of trailing pole parameter m is determined according to n, takes m=n/
It 10 and is rounded, ifThen sample belongs to thin tail distribution；IfThen sample meets thick tail distribution.It will be in step (1)
All sections splicing spectrum in normal g-load by above method, by calculating,Obvious complete section face splicing spectrum
Middle normal g-load meets thick tail distribution.
Thick tail has been carried out to sample by both the above method to detect, and shows that sample data has thick tail characteristic.
(22) sample data known to step (21) meets thick tail distribution, to three kinds of classical Extreme Load Distributions distribution theorys
(district's groups maximum model (Block Maxima Method), independent storm model (Method of Independent
Storms), superthreshold model (Peak Over Threshold)) it compares.Wherein, district's groups maximum model is only chosen on a small quantity
Extreme Load Distributions cause data waste, can not represent the distribution situation of Extreme Load Distributions as sample data；Independent storm model
It is larger to sample data required amount, unstable, engineer application difficulty is estimated for extreme value；Superthreshold model can make full use of extreme value
Load data, practical application is also relatively simple, so this model being most widely used on engineer application.
Based on the above comparison, superthreshold model (abbreviation POT) Lai Jianli aero-engine normal g-load coefficient spectrum is used herein
Mixture Distribution Model.Then the Mixture Distribution Model of aero-engine normal g-load coefficient spectrum is established using superthreshold model,
Assuming that sum is the normal g-load x of ni: x1,x2,…,xi,…,xn(1≤i≤n) is independent identically distributed random change
Sample is measured, overall distribution function F (x is obeyedi) mathematical distribution, u is an abundant big threshold value, and load value is more than threshold value in sample
The number of samples of u is Nu；If xi> u, then claim xiFor superthreshold, y=xi- u be plussage, claim plussage be distributed as condition beyond point
Cloth function Fu(y):
Wherein: P (xi-u≤y|xi> u) it is xiWhen > u, xiThe conditional probability of≤y+u；
That is:
The overall distribution function for indicating sample beyond distribution function with condition, indicates are as follows:
F(xi1-F)=[(u)] × Fu(y)+F(u) (23)
Wherein, xi>u,0≤y≤xi-u；
If overall distribution function F (x) be it is known, pole can be described by the distribution of superthreshold and the distribution of plussage
It is worth sample.However, engineering actual use in, F (x) be usually it is unknown, therefore, to the Limit Distribution of plussage and superthreshold
Research is just particularly important.
(3) flight revolving speed splicing spectrum and normal g-load coefficient splicing spectrum are combined, maneuver classes interlude splicing spectrum 100% is extracted
Corresponding normal g-load coefficient value is as threshold data library at revolving speed；Take the normal g-load that frequency of occurrence is most in threshold data library
Threshold value of the coefficient value as the type aero-engine normal g-load coefficient Mixture Distribution Model；
Step (3) specific steps are as follows:
No matter which kind of Extreme Load Distributions distributed model selected, the selection of threshold value is all important one of step.Threshold of the invention
It is worth choosing method, is to be actually used to choose according to aero-engine, in conjunction with reality, has more physical significance.Rotating speed spectrum and overload
Spectrum all be reflection engine actual use situation, such as Fig. 5 it can be seen that while with rotation speed change, normal g-load spectrum also with
Change.So the Extreme Load Distributions of normal g-load spectrum and the maximum (top) speed of rotating speed spectrum have certain synchronism.
The related coefficient of rotating speed spectrum and normal g-load spectrum is obtained by calculation, the two reaches highly relevant, then turns maximum
The corresponding normal g-load coefficient of speed extracts, as threshold data library undetermined；The data in threshold data library undetermined are carried out general
Rate statistics, corresponds to the highest normal g-load coefficient of the frequency of occurrences as threshold value when using maximum (top) speed.By threshold data library undetermined
Data carry out probability statistics, are reasonable as threshold value using the highest normal g-load coefficient of probability and meet real engine reality
Service condition.
In the step (3), the present invention uses the related coefficient calculation method based on rain flow way.Loading spectrum is carried out first
Peak-to-valley value detection, peak-to-valley value detection is one of basic content of data compression, it is therefore an objective to which the peak-to-valley value in data is extracted
Array as next step data processing；Then rain-flow counting is carried out to each load parameter peak-to-valley value extracted, is recycled
Peak-to-valley value after counting, is translated into amplitude and mean value；It deletes small magnitude again later, i.e., is less than each parameter amplitude [minimum
Amplitude+(maximum amplitude-minimum amplitude) × rain stream filters threshold values] load value reject, then amplitude is less than to the normal direction of threshold value
Overload is rejected, and the number of each parameter amplitude number, that is, task segment after deleting small magnitude is obtained；Finally to flight profile, mission profile statistics
Task number of segment carries out correlation statistics, to obtain the related coefficient between revolving speed and normal g-load.
Related coefficient, which calculates, uses the related coefficient calculation method based on rain flow way, and related coefficient is to measure phase between multi-parameter
The index of pass degree indicates that value is between -1~1, the not equidistant metric of related coefficient with alphabetical r, one
Alphabetic data needs biggish sample size, can just obtain more reliable related coefficient numerical value, In when calculating related coefficient
In mathematical statistics, generally use to calculate the related coefficient of two groups of sample datas.When calculating the related coefficient of two groups of samples, it is necessary to
Guarantee that the sample size of two groups of data is identical, normal g-load xiWith revolving speed yiCoefficient of relationship r are as follows:
In formula,Average is overloaded for discovery,For revolving speed average.
It is obtained by calculation, normal g-load coefficient and engine speed related coefficient reach 0.8355, learn according to statistics related
Coefficient definition, two groups have reached highly relevant degree of relationship.So determining normal g-load coefficient pole by revolving speed extreme value
The threshold value of value is reasonable and meets real engine actual use situation.
Simultaneously from Fig. 2 and Fig. 3, it is apparent that normal g-load overwhelming majority Extreme Load Distributions are in maneuver classes mission profile
Among, and course line class maximum normal g-load coefficient is also no more than 2.So only with by 100% revolving speed pair of maneuver classes mission profile
The normal g-load the answered normal g-load Coefficient Extremum load distribution for statistical analysis that can obtain whole sample.
It is composed relative to normal g-load, the extreme value of rotating speed spectrum is relatively easy to distinguish, so we can will spell among maneuver classes
The corresponding normal g-load coefficient of 100% revolving speed of spectrum is connect to screen.As shown in Figure 8.
Probability statistics are carried out as shown in figure 9, can to more than 100% revolving speed of maneuver classes rotating speed spectrum corresponding normal g-load coefficient
Probability density when finding out that normal g-load coefficient is 2.4270 reaches maximum, thus threshold value be chosen for 2.4270 can be preferable
Meet engine to actually use regular and more accurately carry out distribution research to Extreme Load Distributions.
(4) the normal g-load coefficient for being greater than threshold value in all sections splicing spectrum is defined as Extreme Load Distributions, less than threshold value
Normal g-load coefficient is defined as middle low load, obtain in low, Extreme Load Distributions mixed distributions.
Step (4) specific steps are as follows:
It for middle low load, chooses Two-parameter Weibull Distribution and is fitted, there is thick tail characteristic for Extreme Load Distributions, adopt
With having the mathematical distribution of thick tail characteristic to be fitted it, low load obeys the generalized extreme value point with thick tail characteristic in setting
Cloth (GEV), therefore, overall distribution function is mixed by Two-parameter Weibull Distribution and generalized extreme value distribution, mixed distribution
Function Fmix(x) are as follows:
Wherein, Fw(x, η, β) is Two-parameter Weibull Distribution, and η is scale parameter；β is in Two-parameter Weibull Distribution
Form parameter (η > 0, β > 0)；FGEV(x, u, σ, ξ) is generalized extreme value distribution, and ξ is the form parameter in generalized extreme value distribution；μ is
Location parameter；σ is dimensional parameters；U is threshold value；X is the element in all sections splicing spectrum.
Two-parameter Weibull Distribution cumulative distribution function fw(x) are as follows:
Generalized extreme value cumulative distribution function fGEV(x) are as follows:
Middle low load data statistics figure is as shown in Figure 10.Its cumulative probability is fitted, fitting result is as shown in figure 11.
Available from fitting result: coefficient of multiple correlation R=0.9896 being fitted, fitting result are good.So as to obtain method
Middle low load to overload factor less than 2.4270 obeys η=1.467, the Two-parameter Weibull Distribution of β=3.346.
Extreme Load Distributions data statistics figure is as shown in figure 12.Its cumulative probability is fitted, fitting result is as shown in figure 13.
It is available from fitting result: coefficient of multiple correlation R=0.9982 being fitted, it is possible to find out that fitting result is preferable.From
And it obtains Extreme Load Distributions of the normal g-load value greater than 2.4270 and obeys μ=2.726, σ=0.3651, the CENERALIZED POLAR of ξ=0.06616
Distribution value.
Finally, it should be noted that the above description is only a preferred embodiment of the present invention, it is not used to be the present invention any
Formal limitation.Any research for being familiar with this field and technical staff, in the feelings for not departing from technical solution of the present invention range
Under condition, the non-innovative variation and modification that technical solution of the present invention is made using above content, such as only change raw material examination
Agent adding proportion, reaction duration and operating process etc., should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of with the relevant aero-engine loading spectrum Mixture Distribution Model method for building up of use, which is characterized in that including with
Lower step:
(1) the actual measurement normal direction overload factors of several sections of aero-engine spectrum is gone to be divided into rotating speed spectrum take off, be intermediate,
Land section, all sections and maneuver classes interlude be subjected to ending splicing, obtain normal g-load all sections splicing spectrum with it is motor-driven
Class interlude splicing spectrum；
(2) spectrum is spliced to all sections and carries out frequency statistics, the distribution characteristics of tail data is obtained to analysis of statistical results, then right
Normal g-load coefficient splicing spectrum carries out thick tail detection, determines its distribution, and establish corresponding Mixture Distribution Model；
(3) flight revolving speed splicing spectrum and normal g-load coefficient splicing spectrum are combined, maneuver classes interlude splicing 100% revolving speed of spectrum is extracted
Locate corresponding normal g-load coefficient value as threshold data library；Take the normal g-load coefficient that frequency of occurrence is most in threshold data library
It is worth the threshold value as the type aero-engine normal g-load coefficient Mixture Distribution Model；
(4) the normal g-load coefficient for being greater than threshold value in all sections splicing spectrum is defined as Extreme Load Distributions, less than the normal direction of threshold value
Overload factor is defined as middle low load, obtain in low, Extreme Load Distributions mixed distributions.
2. it is according to claim 1 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, step (1) specific steps are as follows:
(11) research object is the distribution of normal g-load spectrum loading, and flight mission profile is divided into maneuver classes and course line according to actual use
Class, the revolving speed and normal g-load of maneuver classes mission profile are composed, and rotation speed change feature is that interlude has more revolving speed acutely to become
Change, corresponding normal g-load load characteristic is that interlude has a more Extreme Load Distributions variation, the revolving speed of course line generic task section with
Normal g-load spectrum, the feature of rotation speed change are that interlude rotation speed change is smaller, and corresponding normal g-load load characteristic also table
It is now little for load change amplitude, and normal g-load coefficient is all smaller, but the section of taking off and landing of both types mission profile
The feature that section is shown is with uniformity, i.e. normal g-load coefficient is all less than normal；
(12) flight mission profile is divided into three sections, is followed successively by section of taking off, interlude and landing section, and the division of task segment needs
Engine speed spectrum, normal g-load spectrum are compared into division jointly, section of taking off is defined as reaching when revolving speed is started from scratch
After maximum (top) speed, when revolving speed drops to steady state value, it is believed that section of taking off terminates；When revolving speed is begun to decline and does not return to maximum
Revolving speed, and gradually decrease to zero, it is believed that this section is landing section；Remainder is interlude；
(13) all sections are spliced, obtains all section splicing spectrums；Section of taking off and landing section part normal g-load are less than normal,
The distribution of normal g-load Extreme Load Distributions is not influenced, by section of taking off and landing section removal, by several removal section of taking off and landing
Revolving speed and the normal g-load spectrum of the maneuver classes mission profile of section carry out head and the tail splicing, obtain maneuver classes interlude splicing spectrum.
3. it is according to claim 2 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, in the step (12), section of taking off revolving speed drops to steady state value, and the steady state value is the 5% of maximum (top) speed.
4. it is according to claim 1 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, step (2) specific steps are as follows:
(21) all section normal direction overload factor splicing spectrums obtained in step (1) are for statistical analysis, obtain frequency
Secondary statistical chart carries out " thick tail distribution " detection to sample data, learns that sample data meets " thick tail distribution "；
(22) Mixture Distribution Model of aero-engine normal g-load coefficient spectrum is then established using superthreshold model,
Assuming that sum is the normal g-load x of ni: x1,x2,…,xi,…,xn(1≤i≤n) is independent identically distributed stochastic variable sample
This, obeys overall distribution function F (xi) mathematical distribution, u is an abundant big threshold value, and load value is more than threshold value u's in sample
Number of samples is Nu；If xi> u, then claim xiFor superthreshold, y=xi- u is plussage, and plussage is claimed to be distributed as condition beyond distribution
Function Fu(y):
Wherein: P (xi-u≤y|xi> u) it is xiWhen > u, xiThe conditional probability of≤y+u；
That is:
The overall distribution function for indicating sample beyond distribution function with condition, indicates are as follows:
F(xi1-F)=[(u)] × Fu(y)+F(u) (3)
Wherein, xi>u,0≤y≤xi-u。
5. it is according to claim 4 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, the thickness tail detection method has Q-Q figure method and trailing pole value index number method.
6. it is according to claim 5 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, the specific steps of the Q-Q figure method are as follows:
(a) sum is set as the normal g-load x of ni:x1,x2,…,xi,…,xn(1≤i≤n) meets normal distribution, quantile qiAre as follows:
Wherein, pi=(i-1/2)/n is xi≤qiProbability；I=1,2 ..., n is i-th of element of sample；E is natural constant；
π is pi；
(b) sample data is arranged from small to large, is obtained: x11,x12,…,x1n, corresponding probability value is p1=(1-1/2)/
n,p2=(2-1/2)/n ..., pn=(n-1/2)/n；Corresponding normal state quantile q is calculated according to formula (4)1,q2,…,
qn, by several to (qi,x1i), (i=1,2 ... n) depict on a coordinate plane, and sample fractiles increase than normal state point
Cloth is fast, and apparent convex trend is presented in sample fractiles number curve, then the sample data has thick tail characteristic.
7. it is according to claim 5 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, the specific steps of the trailing pole value index number method are as follows:
If the normal g-load that sum is n is xi:x1,x2,…,xi,…,xn(1≤i≤n), in which: i is i-th of element in ordered series of numbers；
Sample data is arranged from small to large and is obtained: x11,x12,…,x1n, then, the Monent type estimator of sampleExpression formula are as follows:
Wherein, trailing pole coefficient
Trailing pole coefficientThe value of trailing pole parameter m is determined according to n, is taken m=n/10 and is taken
It is whole, ifThen sample belongs to thin tail distribution；IfThen sample meets thick tail distribution.
8. it is according to claim 1 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, step (3) specific steps are as follows:
The related coefficient of rotating speed spectrum and normal g-load spectrum is obtained by calculation, the two reaches highly relevant, then by maximum (top) speed pair
The normal g-load coefficient answered extracts, as threshold data library undetermined；The data in threshold data library undetermined are subjected to probability system
Meter, corresponds to the highest normal g-load coefficient of the frequency of occurrences as threshold value when using maximum (top) speed.
9. it is according to claim 8 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, in the step (3), related coefficient, which calculates, uses the related coefficient calculation method based on rain flow way, related coefficient
It is the index of degree of correlation between measuring multi-parameter, is indicated with alphabetical r, value is an alphabetic data between -1~1,
Normal g-load xiWith revolving speed yiCoefficient of relationship r are as follows:
In formula,Average is overloaded for discovery,For revolving speed average.
10. it is according to claim 5 to use relevant aero-engine loading spectrum Mixture Distribution Model method for building up,
It is characterized in that, step (4) specific steps are as follows:
It for middle low load, chooses Two-parameter Weibull Distribution and is fitted, there is thick tail characteristic for Extreme Load Distributions, using tool
There is the mathematical distribution of thick tail characteristic to be fitted it, low load obeys the generalized extreme value distribution with thick tail characteristic in setting,
Overall distribution function is mixed by Two-parameter Weibull Distribution and generalized extreme value distribution, mixed distribution function Fmix(x) are as follows:
Wherein, Fw(x, η, β) is Two-parameter Weibull Distribution, and η is scale parameter；β is the shape ginseng in Two-parameter Weibull Distribution
Number (η > 0, β > 0)；FGEV(x, u, σ, ξ) is generalized extreme value distribution, and ξ is the form parameter in generalized extreme value distribution；μ is position ginseng
Number；σ is dimensional parameters；U is threshold value；X is the element in all sections splicing spectrum；
Two-parameter Weibull Distribution cumulative distribution function fw(x) are as follows:
Generalized extreme value cumulative distribution function fGEV(x) are as follows:
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