CN106777696B

CN106777696B - Design Method of Flutter based on QMU

Info

Publication number: CN106777696B
Application number: CN201611174664.5A
Authority: CN
Inventors: 杨婧; 张保强; 陈庆; 苏国强
Original assignee: Xiamen University
Current assignee: Xiamen University
Priority date: 2016-12-19
Filing date: 2016-12-19
Publication date: 2019-05-17
Anticipated expiration: 2036-12-19
Also published as: CN106777696A

Abstract

Design Method of Flutter based on QMU is related to uncertain and nargin quantification technique.1) finite element model of structure is established；2) flutter speed of certainty condition flowering structure is calculated by commercial finite element software, and divided by certain safety coefficient as Flutter Boundaries；3) the flutter distribution under the influence of stochastic uncertainty is described by probability distribution；4) it is based on flutter speed probability distribution, quantifies the uncertain degree and nargin of flutter speed by QMU technology, and obtains confidence factor CR, as Flutter Boundaries safety evaluation foundation；5) safe range of cognition uncertain factor is solved by confidence factor, take the probabilistic two parameter sections of cognition, it is divided into the section of n × n, m sample calculation is carried out to stochastic uncertainty parameter in each section and interpolation obtains the curve of CR=1 and CR=2, marks off the uncertain factor range for ensuring flutter safety and the influence of quantization uncertainty factor to a certain extent.

Description

Design Method of Flutter based on QMU

Technical field

The present invention relates to uncertain and nargin quantification techniques, more particularly, to a kind of Design Method of Flutter based on QMU.

Background technique

Uncertainty is widely present in actual engineering problem, is broadly divided into two classes, and one is stochastic uncertainty, is such as tied The parameter uncertainties such as the material load attribute during structure processing and manufacturing and use, mostly use probability distribution to describe；Two It is uncertain for cognition, it is that section distribution description is mostly used due to the uncertainty that knowledge is limited and generates.It is most of at present Research is just in stochastic uncertainty, and in fact the uncertain influence to result of cognition is equally very important.Flutter is The most noticeable problem of aeroelastic stability research field.Aircraft occur flutter be it is breakneck, when flying speed is super When crossing flutter critical speed, amplitude, which swashs to increase severely, to be added, it might even be possible to quickly destroy an airplane.Aircraft is in flight envelope Do not allow to occur any type of flutter, but Flutter Boundaries again cannot overly conservative influence flying quality, therefore according to performance and Index is reasonably designed containing probabilistic parameter is recognized, to guarantee that Flutter Boundaries i.e. safety is not again overly conservative to Guan Chong It wants.

QMU (quantification of margins and uncertainties, it is uncertain to quantify skill with nargin Art) it is that the National Nuclear Security Administration of U.S. Department of Energy subordinate in 2001 combines Los Alamos, Lao Lunsi Lawrence Livermore New method (Pilch M, Trucano T G, the Helton J C.Ideas proposed with the sub- three power laboratories in the Holy Land underlying quantification of margins and uncertainties(QMU):a white paper[J] .Unlimited Release SAND2006-5001,Sandia National Laboratory,Albuquerque,New Mexico, 2006,87185:2.), for assessing the reliability and safety of inventory's nuclear weapon in the insufficient situation of experimental data Property.QMU method is using product normal operation as research object, based on physics model of failure and margin design, it is believed that make be System reaches required performance, it is necessary to be directed to known potential failure mode, enough design margins be reserved for system, to ensure to be System is absolutely reliable, but when calculated performance allowance M, will receive a variety of random and cognition uncertain factor influence, Once these uncertain integrated values are greater than performance margin M, product may generate trouble or failure.Confidence is used in QMU The ratio of factor CR, i.e. performance margin M and not true foot U characterizes this relationship between performance margin and uncertainty, when When CR > 1, it is believed that system is safe.This method can be used as under condition of uncertainty, the peace of flight structure flutter margin Full property assesses foundation, and is designed based on this to cognition uncertain parameters.

Summary of the invention

The purpose of the invention is to overcome deficiencies of the prior art, a kind of flutter based on QMU is provided and is set Meter method.

The present invention the following steps are included:

1) finite element model of structure is established；

2) flutter speed of certainty condition flowering structure is calculated by commercial finite element software, and is divided by certain safety Number is used as Flutter Boundaries；

3) the flutter distribution under the influence of stochastic uncertainty is described by probability distribution.Consider related ginseng in finite element model Several uncertainties, such as elasticity modulus, shearing rigidity is as stochastic uncertainty, and density of material, atmospheric density ratio is as cognition Uncertainty, using the probability distribution of Monte Carlo methods of sampling quantization stochastic uncertainty flutter speed.

4) it is based on flutter speed probability distribution, quantifies the uncertain degree and nargin of flutter speed by QMU technology, and obtain To confidence factor CR, as Flutter Boundaries safety evaluation foundation；

5) safe range that cognition uncertain factor is solved by confidence factor takes probabilistic two parameters of cognition Section is divided into the section of n*n, carries out m sample calculation to stochastic uncertainty parameter in each section and interpolation obtains CR The curve of=1 and CR=2 marks off the uncertain factor range for ensuring flutter safety and quantifies to a certain extent uncertain The influence of sexual factor.

In step 4), uncertainty quantization and QMU appraisal procedure are as follows:

(1) stochastic uncertainty of flutter speed, uncertainty are indicated by probability distribution are as follows:

The flutter speed that Flutter Boundaries are obtained by deterministic parameters calculation is multiplied by obtained by certain safety coefficient K, it is assumed that there is also Stochastic uncertainty is described by probability distribution, the accounting equation of uncertainty are as follows:

The then uncertainty calculation equation of whole system are as follows:

Wherein, V indicates to consider the flutter speed probability distribution of stochastic uncertainty, and VL indicates quivering multiplied by safety coefficient K The Cumulative Distribution Function on vibration boundary, P indicate that probability, β indicate certain confidence level, generally take 0.95.

(2) nargin quantifies, safe distance of the nargin between Flutter Boundaries and the probability distribution of flutter speed, calculating side Journey are as follows:

(3) confidence factor is solved for judging flutter margin safety, the accounting equation of confidence factor are as follows:

In QMU technology, when CR is greater than 1, it is believed that system safety, then defined Flutter Boundaries have enough nargin to cover Uncertainty can be used as the criterion of Flutter Boundaries safety evaluation.

Under conditions of the present invention is existed simultaneously suitable for stochastic uncertainty and cognition uncertainty, to guarantee Flutter Boundaries The premise of safety, design contain the probabilistic parameter of cognition.Consider that various mixing present in structure and flying condition are not true It qualitatively influences, flutter safety is assessed based on QMU technology, further the safe edge of quantization cognition uncertain parameters Boundary, and Design cognition uncertain parameters.

Compared with the prior art, the invention has the advantages that:

1) uncertain quantization is carried out based on finite element software, computational efficiency is high, easy to operate.

2) QMU considers the uncertainty of flutter speed and Flutter Boundaries simultaneously, and the safety criterion as Flutter Problem can Reliability is high.

3) can intuitively quantify to recognize probabilistic influence, and it is not true to provide on the basis of guarantee system safety cognition The scope of design of qualitative parameter.

Detailed description of the invention

Fig. 1 is AGARD445.6 wing figure.

Fig. 2 is the flutter speed probability distribution considered under stochastic uncertainty.

Fig. 3 is the QMU considered under stochastic uncertainty.

Fig. 4 is cognition uncertain parameters and CR relational graph.

Specific embodiment

The stochastic uncertainty of flutter speed quantifies specific implementation step

1, the finite element mould of AGARD445.6 wing structure is established using commercial finite element software Patran and Nastran Type, for the model as shown in Figure 1, air-foil is NACA 65A004, relevant parameter is as shown in table 1, and deterministic parameter is calculated Under flutter speed V_F, and Flutter Boundaries V is calculated according to required safety coefficient K_F', and assume that it has certain do not know Property, it is described using random distribution, the VL curve on the left of Fig. 3.

Table 1

Elastic modulus E₁₁	Elastic modulus E₂₂	Shearing rigidity G₁₂	Poisson's ratio υ	Density of material φ	Atmospheric density ratio r
						4.16×10⁸Pa	3.151×10⁹Pa	4.392×10⁸Pa	0.31	381.98Kg/m³	0.3486

2, consider to compile using Monte Carlo nesting circulation 10000 times based on Matlab such as the stochastic uncertainty in table 2 Journey reads in parameter information from the * .bdf file of Nastran and is modified to parameter to introduce uncertainty, called commercial Finite element software Nastran carries out FLUTTER CALCULATION；Flutter speed is read in from destination file * .f06, every circulation primary obtains one A flutter speed finally obtains the cumulative distribution function of a flutter speed, forms the probability distribution of Fig. 2 flutter speed.

Table 2

Parameter	Distribution	Uncertain type
			Elastic modulus E₁₁	Normal state	At random
Elastic modulus E₂₂	Normal state	At random
			Shearing rigidity G₁₂	Normal state	At random

Flutter parameters design method specific implementation process based on QMU includes:

1, QMU uncertainty quantization and nargin quantization as shown in figure 3, by formula (1) (2) be calculated uncertainty and The ratio C R of nargin and confidence factor, as CR > 1, it is believed that quivering under current level of uncertainty, safety coefficient K Vibration boundary is safe.

2, it will divide equally in atmospheric density ratio and the density of material two probabilistic ranges of variables of cognition and obtain 10 points, That is, a total of 100 variable combination uncertain for cognition.For each combination, other three random parameters are considered Uncertainty under the influence of CR value.100 laggard row interpolations of CR value are being obtained, the curve of CR=1 and CR=2 are obtained, 1 < CR < 2 are within the scope of this it is considered that current design is safety and not overly conservative, as shown in figure 4, and can therefrom determine Property judge influence of the uncertain amount of two cognitions for CR value and flutter safety, and measured under the premise of flutter safety The range for changing cognition uncertain parameters, to Design cognition uncertain parameters.

Claims

1. the Design Method of Flutter based on QMU, it is characterised in that the following steps are included:

1) finite element model of structure is established；

2) flutter speed of certainty condition flowering structure is calculated by commercial finite element software, and is made divided by certain safety coefficient For Flutter Boundaries；

3) the flutter distribution under the influence of stochastic uncertainty is described by probability distribution, considers relevant parameter in finite element model Uncertainty, described uncertain uncertain including stochastic uncertainty and cognition, the stochastic uncertainty includes elastic Modulus and shearing rigidity；The uncertain cognition includes density of material and atmospheric density ratio；

4) it is based on flutter speed probability distribution, quantifies the uncertain degree and nargin of flutter speed by QMU technology, and is set Factor CR is believed, as Flutter Boundaries safety evaluation foundation；Uncertainty quantization and QMU appraisal procedure are as follows:

The flutter speed that Flutter Boundaries are obtained by deterministic parameters calculation is multiplied by obtained by certain safety coefficient K, it is assumed that there is also random Uncertainty is described by probability distribution, the accounting equation of uncertainty are as follows:

The then uncertainty calculation equation of whole system are as follows:

Wherein, V indicates to consider the flutter speed probability distribution of stochastic uncertainty, and VL indicates the flutter side multiplied by safety coefficient K The Cumulative Distribution Function on boundary, P indicate that probability, β indicate certain confidence level, take 0.95；

(2) nargin quantifies, safe distance of the nargin between Flutter Boundaries and the probability distribution of flutter speed, accounting equation Are as follows:

In QMU technology, when CR is greater than 1, it is believed that system safety, then defined Flutter Boundaries have enough nargin to cover not really Fixed degree, the criterion as Flutter Boundaries safety evaluation；

5) safe range that cognition uncertain factor is solved by confidence factor takes probabilistic two parameter regions of cognition Between, it is divided into the section of n × n, m sample calculation is carried out to stochastic uncertainty parameter in each section and interpolation obtains CR= The curve of 1 and CR=2 marks off the uncertain factor range for ensuring flutter safety and to a certain extent quantization uncertainty The influence of factor.