CN106599491A - QMU-based flutter margin evaluation method - Google Patents

Abstract

The invention discloses a QMU-based flutter margin evaluation method, and relates to a quantification technology of uncertainties and margins. The flutter margin evaluation method comprises the following steps of 1) establishing a finite element model of a structure; 2) calculating a flutter speed of the structure in a certainty condition through commercial finite element software, and reserving a certain margin K as a flutter border; 3) describing flutter distribution under influence of mixed uncertainties through a probability box, and considering uncertainties of related parameters in the finite element model, wherein the uncertainties comprise accidental uncertainties and epistemic uncertainties; the accidental uncertainties comprise elasticity modulus and shearing rigidity; the epistemic uncertainties comprise the ratio of a material density to an air density; and obtaining probability box distribution of the flutter speed by adopting a Monte Carlo sampling method, wherein a result under joint effect of two kinds of uncertainties is included; and 4) based on the probability box distribution, performing quantification on uncertainties and margins of the flutter speed through the QMU technology, and obtaining a confidence factor (CF) to be taken as the flutter border safety evaluation basis.

Description

A kind of flutter margin appraisal procedure based on QMU

Technical field

The present invention relates to uncertain and allowance quantification technique, assesses more particularly, to a kind of flutter margin based on QMU Method.

Background technology

Uncertainty is widely present in actual engineering problem, is broadly divided into two classes, and one is accidentally uncertainty, also referred to as For stochastic uncertainty, the material load attribute parameter uncertainty such as during structure processing and manufacturing and use is more Described using probability distribution；Two is cognitive uncertain, is the uncertainty produced because knowledge is limited, more using interval point Cloth is described.For the simultaneous situation of two kinds of uncertainties can be quantified using probability box.Flutter is dynamic aeroelastic The most noticeable problem in stability study field.It is breakneck that aircraft occurs flutter, when flying speed is faced more than flutter During boundary's speed, amplitude swashs sharp increase and adds, it might even be possible to quick to destroy an airplane.Aircraft does not allow to send out in flight envelope Any type of flutter of life, therefore it is most important to determine suitable Flutter Boundaries how to quantify all kinds of uncertainties.It is beautiful at present The military of state takes 15% nargin as Flutter Boundaries, and this standard is continued to use from modern from nineteen sixty, and in recent years aircraft mobility will Ask and increasingly improve, this standard is unfavorable for the improvement in aircraft operation performance, thus how to obtain in safe and reliable premise Under relax Flutter Boundaries and receive more and more attention.

QMU (quantification of margins and uncertainties, it is uncertain to quantify skill with allowance Art) for calendar year 2001 USDOE subordinate National Nuclear Security Administration joint Los Alamos, Lao Lunsi Lawrence Livermores New method (Pilch M, Trucano T G, the Helton J C.Ideas that three power laboratory sub- with the Holy Land proposes underlying quantification of margins and uncertainties(QMU):a white paper[J] .Unlimited Release SAND2006-5001,Sandia National Laboratory,Albuquerque,New Mexico,2006,87185:2.), it is used to assess the reliability and safety of stock's nuclear weapon in the case of experimental data deficiency Property.QMU methods normally operate to research object with product, based on physics model of failure and margin design, it is believed that to make be System reaches required performance, it is necessary to be that system reserves enough design margins, to guarantee to be for known potential failure mode System is definitely reliable, but when performance margin M is calculated, can be affected by various random and cognitive uncertain factors, Once these uncertain integrated values are more than performance margin M, product may produce trouble or failure.Confidence is adopted in QMU The ratio of factor CR, i.e. performance margin M and not true foot U characterizing this relation between performance margin and uncertainty, when CR>When 1, it is believed that system is safe.The method can be used as under condition of uncertainty, the peace of flight structure flutter margin Full property assessment, as the theoretical foundation for relaxing flutter margin border.

The content of the invention

The invention aims to overcome deficiencies of the prior art, there is provided a kind of flutter based on QMU is abundant Degree appraisal procedure.

The present invention is comprised the following steps：

1) FEM model of structure is set up；

2) flutter speed of structure under the conditions of certainty is calculated by commercial finite element software, and leaves certain nargin K As Flutter Boundaries；

3) the flutter distribution under the influence of Hybrid parameter matrix is described by probability box, it is considered to relevant parameter in FEM model Uncertainty, it is described it is uncertain include that accidentally uncertain and cognition is uncertain, it is described accidental uncertain to include bullet Property modulus and shearing rigidity；The cognitive uncertainty includes density of material and atmospheric density ratio；Using Monte Carlo sampling side Method obtains the probability box distribution of flutter speed, wherein comprising the result under two kinds of uncertain collective effects；

4) it is distributed based on probability box, the uncertain degree and allowance of flutter speed is quantified by QMU technologies, and obtains confidence Factor CR, as Flutter Boundaries safety evaluation foundation.

In step 4) in, it is described based on probability box be distributed, by QMU technologies quantify flutter speed uncertain degree with it is abundant Amount, and confidence factor CR is obtained, it is as follows as the concrete grammar of Flutter Boundaries safety evaluation foundation：

(1) uncertainty quantifies：

The Hybrid parameter matrix of flutter speed is represented by probability box, its uncertainty is：

Flutter Boundaries are multiplied by certain safety coefficient by the flutter speed that deterministic parameters calculation is obtained, and (safety coefficient is according to nargin K takes) gained, it is assumed that it there is also uncertainty, and the accounting equation of its uncertainty is：

Then the uncertainty calculation equation of whole system is：

Wherein, V_rightRepresent the right margin in the distribution of flutter speed probability box, V_leftRepresent the distribution of flutter speed probability box In left margin, VL represents the Cumulative Distribution Function of Flutter Boundaries.P represents probability, and β represents certain confidence level, typically takes 0.95.

(2) quantization of allowance：Allowance is the safe distance between Flutter Boundaries and the probability box distribution of flutter speed, and it is counted Calculating equation is：

(3) solving confidence factor is used to judge flutter margin security that the accounting equation of confidence factor to be：

In QMU technologies, when CR is more 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.

The impact of various Hybrid parameter matrix present in structure and flying condition is considered, based on QMU technologies, there is provided a kind of Flutter margin security assessment method, further to relax Flutter Boundaries, improves the flying quality of flight structure.

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) probability cassette method can simultaneously consider two kinds of uncertainties present in engineering, provide simple and clear quantization As a result.

3) QMU considers the uncertainty of flutter speed and Flutter Boundaries simultaneously, with a high credibility, it is contemplated that Flutter Problem it is tight Principal characteristic, the method is more insured as the security criterion for relaxing Flutter Boundaries.

Description of the drawings

Fig. 1 is AGARD445.6 wing figures.

Fig. 2 is to consider the flutter speed probability box distribution under Hybrid parameter matrix.

Fig. 3 is to consider the QMU under Hybrid parameter matrix.

Specific embodiment

Hybrid parameter matrix based on probability box quantifies specific implementation step to be included：

1st, the finite element mould of AGARD445.6 wing structures is set up using commercialization finite element software Patran and Nastran Type, the model is as shown in figure 1, wing wing root chord length 558.8mm, wing tip chord length 368.3mm, the long 762mm of the span, a quarter String of a musical instrument wing setting is 45 degree, is NACA 65A004 along aerofoil profile is flowed to, and relevant parameter as shown in table 1, is calculated certainty Flutter speed V under parameter_F, and nargin K according to required checking is calculated Flutter Boundaries V_F’。

Table 1

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

2nd, consider the uncertainty such as table 2, sampled using the nested circulation 100 × 1000 in Monte Carlo, outer layer is recognized for 100 times Know uncertainty, internal layer is sampled to stochastic uncertainty 1000 times, programmed based on Matlab, from the * .bdf files of Nastran Read in parameter information and parameter is modified to introduce uncertainty, call commercial finite element software Nastran to carry out flutter Calculate；Flutter speed is read in from destination file * .f06, internal layer obtains a flutter speed per circulation primary, and outer layer is often circulated The cumulative distribution function of a flutter speed is once obtained, 100 Cumulative Distribution Functions are finally obtained, Fig. 2 flutter speeds are constituted Probability box distribution.

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
Atmospheric density compares r	It is interval	It is cognitive
			Density of material φ	It is interval	It is cognitive

Included based on the flutter margin appraisal procedure specific implementation process of QMU：

1st, assume that Flutter Boundaries there is also certain uncertainty, described using random distribution, such as the VL of Fig. 3 leftmost sides is bent Line.

2nd, QMU uncertainty quantify and allowance quantify as shown in figure 3, by formula (1) (2) be calculated uncertainty with Allowance, and ratio C R of confidence factor, work as CR>When 1, it is believed that in current level of uncertainty, take the Flutter Boundaries under nargin K It is safe.

Claims (2)

1. a kind of flutter margin appraisal procedure based on QMU, it is characterised in that comprise the following steps：

1) FEM model of structure is set up；

2) flutter speed of structure under the conditions of certainty is calculated by commercial finite element software, and leaves certain nargin K conduct Flutter Boundaries；

3) the flutter distribution under the influence of Hybrid parameter matrix is described by probability box, it is considered to which relevant parameter is not in FEM model Certainty, described uncertain uncertain including accidentally uncertain and cognition, the accidental uncertainty includes springform Amount and shearing rigidity；The cognitive uncertainty includes density of material and atmospheric density ratio；Obtained using the Monte Carlo methods of sampling Probability box to flutter speed is distributed, wherein comprising the result under two kinds of uncertain collective effects；

4) it is distributed based on probability box, the uncertain degree and allowance of flutter speed is quantified by QMU technologies, and obtains confidence factor CR, as Flutter Boundaries safety evaluation foundation.

2. as claimed in claim 1 a kind of flutter margin appraisal procedure based on QMU, it is characterised in that in step 4) in, it is described It is distributed based on probability box, the uncertain degree and allowance of flutter speed is quantified by QMU technologies, and obtain confidence factor CR, is made Concrete grammar for Flutter Boundaries safety evaluation foundation is as follows：

(1) uncertainty quantifies：

The Hybrid parameter matrix of flutter speed is represented by probability box, its uncertainty is：

Flutter Boundaries are multiplied by certain safety coefficient by the flutter speed that deterministic parameters calculation is obtained (safety coefficient takes according to nargin K) Gained, it is assumed that it there is also uncertainty, the accounting equation of its uncertainty is：

Then the uncertainty calculation equation of whole system is：

$U=\sqrt{{({\left(V_{right}\right)}_{P=0.5}-{\left(V_{left}\right)}_{P=\frac{1-\mathrm{\β}}{2}})}^2+{({\mathrm{VL}}_{P=\frac{1+\mathrm{\β}}{2}}-{\mathrm{VL}}_{P=0.5})}^2}---\left(1\right)$

Wherein, V_rightRepresent the right margin in the distribution of flutter speed probability box, V_leftIn representing the distribution of flutter speed probability box Left margin, VL represents the Cumulative Distribution Function of Flutter Boundaries；P represents probability, and β represents certain confidence level, typically takes 0.95.

(2) quantization of allowance：Allowance is the safe distance between the probability box distribution of Flutter Boundaries and flutter speed, its calculating side Cheng Wei：

$M=|{\left(V_{left}\right)}_{P=\frac{1-\mathrm{\β}}{2}}-{\left(VL\right)}_{P=\frac{1+\mathrm{\β}}{2}}|---\left(2\right)$

(3) solving confidence factor is used to judge flutter margin security that the accounting equation of confidence factor to be：

$CR=\frac{M}{U}---\left(3\right)$

In QMU technologies, when CR is more than 1, it is believed that system safety, then to have enough nargin to cover not true for defined Flutter Boundaries Fixed degree, can be used as the criterion of Flutter Boundaries safety evaluation.