CN106599491B

CN106599491B - Flutter margin evaluation method based on QMU

Info

Publication number: CN106599491B
Application number: CN201611174665.XA
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: 2020-05-15
Anticipated expiration: 2036-12-19
Also published as: CN106599491A

Abstract

A flutter margin evaluation method based on QMU relates to uncertainty and margin quantization technology. The method comprises the following steps: 1) establishing a finite element model of the structure; 2) calculating the flutter speed of the structure under the deterministic condition through commercial finite element software, and reserving a certain margin K as a flutter boundary; 3) describing flutter distribution under the influence of mixing uncertainty through a probability box, and considering uncertainty of related parameters in a finite element model, wherein the uncertainty comprises accidental uncertainty and cognitive uncertainty, and the accidental uncertainty comprises elastic modulus and shear stiffness; the cognitive uncertainty comprises a material density and an air density ratio; obtaining probability box distribution of flutter speed by adopting a Monte Carlo sampling method, wherein the probability box distribution comprises results under the combined action of two uncertainties; 4) based on probability box distribution, the uncertainty and the allowance of the flutter speed are quantified through a QMU technology, and a confidence factor CR is obtained and used as a flutter boundary safety evaluation basis.

Description

Flutter margin evaluation method based on QMU

Technical Field

The invention relates to an uncertainty and margin quantification technology, in particular to a flutter margin evaluation method based on a QMU.

Background

Uncertainty widely exists in practical engineering problems, and is mainly divided into two categories, namely accidental uncertainty, also called random uncertainty, such as uncertainty of parameters such as material load attributes in the processes of structure processing, manufacturing and using, and probability distribution description is mostly adopted; the second is cognitive uncertainty, which is uncertainty due to limited knowledge, and is mostly described by interval distribution. The probability box can be used for quantification of the case where two uncertainties exist simultaneously. Flutter is the most noticeable problem in the field of aeroelastic stability studies. The aircraft is very dangerous to vibrate, and when the flying speed exceeds the flutter critical speed, the amplitude is sharply increased, and even one aircraft can be quickly destroyed. The aircraft is not allowed to flutter in any form within the flight envelope, so how to quantify various types of uncertainty to determine a proper flutter boundary is important. At present, the American military takes a 15% margin as a flutter boundary, the standard is used from 1960, the requirement on the maneuverability of the aircraft is increasingly increased in recent years, the standard is not beneficial to the improvement on the operation performance of the aircraft, and therefore, the attention on how to obtain a wide flutter boundary on the premise of safety and reliability is increased.

QMU (quantification of landmarks and uncertainties, quantification of uncertainty and margin techniques) is a new method proposed by the National Nuclear safety administration, under the U.S. department of energy 2001, in conjunction with the Ross armors, Lawrence Rivermor and san Diego National laboratories (Pilch M, Trucano T G, Helton J C. Ideasurrendering quantification of landmarks and uncertainties (QMU): a white paper [ J ]. Un submitted Release SAD 2006-5001, Sandia National Laboratory, Albuquerque, NewMexico,2006,87185: 2) for assessing reliability and safety of nuclear weapons in inventory in the event of insufficient experimental data. The QMU method is based on the failure physics model and margin design, and it is considered that to achieve the required performance of the system, it is necessary to set aside sufficient design margin for the system to ensure the absolute reliability of the system for the known potential failure mode, but when calculating the performance margin M, the QMU method is affected by various random and cognitive uncertainty factors, and once the comprehensive value of the uncertainty is greater than the performance margin M, the product may fail or fail. This relationship between performance margin and uncertainty is characterized in QMU by a confidence factor CR, i.e. the ratio of performance margin M to uncertainty U, and we consider the system safe when CR > 1. The method can be used for safety evaluation of the flutter margin of the flight structure under the uncertain condition and can be used as a theoretical basis for widening the flutter margin boundary.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide a flutter margin evaluation method based on QMU.

The invention comprises the following steps:

1) establishing a finite element model of the structure;

2) calculating the flutter speed of the structure under the deterministic condition through commercial finite element software, and reserving a certain margin K as a flutter boundary;

3) describing flutter distribution under the influence of mixing uncertainty through a probability box, and considering uncertainty of related parameters in a finite element model, wherein the uncertainty comprises accidental uncertainty and cognitive uncertainty, and the accidental uncertainty comprises elastic modulus and shear stiffness; the cognitive uncertainty comprises a material density and an air density ratio; obtaining probability box distribution of flutter speed by adopting a Monte Carlo sampling method, wherein the probability box distribution comprises results under the combined action of two uncertainties;

4) based on probability box distribution, the uncertainty and the allowance of the flutter speed are quantified through a QMU technology, and a confidence factor CR is obtained and used as a flutter boundary safety evaluation basis.

In step 4), the uncertainty and the margin of the flutter speed are quantified by a QMU technique based on the probability box distribution, and a confidence factor CR is obtained, and the specific method used as the basis for the flutter boundary safety evaluation is as follows:

(1) and (3) uncertainty quantification:

the mixing uncertainty of the flutter speed is represented by a probability box, and the uncertainty is as follows:

the flutter boundary is obtained by multiplying a certain safety factor (the safety factor is obtained according to margin K) by the flutter speed obtained by deterministic calculation, and if uncertainty exists, the calculation equation of the uncertainty is as follows:

the uncertainty calculation equation for the whole system is:

wherein, V_rightIndicating the right boundary, V, in the flutter velocity probability box distribution_leftBox for indicating flutter speed probabilityThe left border in the cloth, VL represents the cumulative distribution function of the flutter border P represents the probability and β represents a certain confidence level, typically 0.95.

(2) And (3) quantification of the margin: the margin is the safe distance between the flutter boundary and the probability box distribution of the flutter speed, and the calculation equation is as follows:

(3) solving a confidence factor for judging the safety of the flutter margin, wherein the calculation equation of the confidence factor is as follows:

in the QMU technology, when CR is greater than 1, the system is considered safe, and the defined chatter boundary has enough margin to cover uncertainty, which can be used as a criterion for safety evaluation of the chatter boundary.

Considering the influence of various mixed uncertainties existing in the structure and flight conditions, based on the QMU technology, a flutter margin safety evaluation method is provided, so that the flutter boundary is further widened, and the flight performance of the flight structure is improved.

Compared with the prior art, the invention has the beneficial effects that:

1) and uncertainty quantification is carried out based on finite element software, so that the calculation efficiency is high and the operation is convenient.

2) The probability box method can simultaneously consider two uncertainties existing in engineering and give visual and clear quantitative results.

3) The QMU considers both the uncertainty of the flutter speed and the flutter boundary, has high reliability, and the method is more safe as a safety criterion for relaxing the flutter boundary in consideration of the severity of the flutter problem.

Drawings

Fig. 1 is an AGARD445.6 airfoil view.

FIG. 2 is a flutter velocity probability box distribution under consideration of mixing uncertainty.

Fig. 3 is a QMU under consideration of the hybrid uncertainty.

Detailed Description

The concrete implementation steps of the probability box-based mixed uncertainty quantification comprise:

1. a finite element model of an AGARD445.6 wing structure is established by using commercial finite element software Patran and Nastran, the model is shown in figure 1, the wing root chord length of the wing is 558.8mm, the wing tip chord length is 368.3mm, the span length is 762mm, the sweepback angle of a quarter-chord wing is 45 degrees, the wing profile along the flow direction is NACA 65A004, relevant parameters are shown in table 1, and the flutter speed V under the deterministic parameters is calculated_FAnd calculating to obtain a flutter boundary V according to a margin K required to be verified_F’。

TABLE 1

Modulus of elasticity E₁₁	Modulus of elasticity E₂₂	Shear stiffness G₁₂	Poisson ratio upsilon	Material density phi	Air density ratio r
						4.16×10⁸Pa	3.151×10⁹Pa	4.392×10⁸Pa	0.31	381.98Kg/m³	0.3486

2. Considering the uncertainty as shown in table 2, using monte carlo nested loop 100 × 1000 sampling, the outer layer is 100 times of cognitive uncertainty, the inner layer is 1000 times of sampling is random uncertainty, based on Matlab programming, reading parameter information from the astran bdf file, modifying the parameters to introduce uncertainty, and calling commercial finite element software, nartran, to perform flutter calculation; reading the flutter speed from the result file f06, obtaining one flutter speed once per cycle of the inner layer, obtaining one accumulative distribution function of the flutter speed once per cycle of the outer layer, and finally obtaining 100 accumulative distribution functions to form probability box distribution of the flutter speed in the figure 2.

TABLE 2

Parameter(s)	Distribution of	Uncertainty type
			Modulus of elasticity E₁₁	Normal (normal)	Random
Modulus of elasticity E₂₂	Normal (normal)	Random
			Shear stiffness G₁₂	Normal (normal)	Random
Air density ratio r	Interval(s)	Cognition
			Material density phi	Interval(s)	Cognition

The specific implementation process of the QMU-based flutter margin evaluation method comprises the following steps:

1. assuming that there is some uncertainty in the dither boundaries, it is described using a random distribution, such as the leftmost VL curve in fig. 3.

2. QMU uncertainty and margin quantization As shown in FIG. 3, the uncertainty and margin, as well as the confidence factor ratio CR, are calculated by equations (1) (2), and when CR >1, it is considered safe to take the chatter boundary at the margin K at the current uncertainty level.

Claims

1. A flutter margin evaluation method based on QMU is characterized by comprising the following steps:

1) establishing a finite element model of the structure;

2) calculating the flutter speed of the structure under the deterministic condition through commercial finite element software, and reserving a margin K as a flutter boundary;

4) based on probability box distribution, the uncertainty and the allowance of the flutter speed are quantified through a QMU technology, a confidence factor CR is obtained and used as a flutter boundary safety evaluation basis, and the specific method comprises the following steps:

4.1 uncertainty quantification:

wherein, V_rightIndicating the right boundary, V, in the flutter velocity probability box distribution_leftRepresenting the left border in the flutter velocity probability box distribution, P representing the probability, β representing the confidence level;

the flutter boundary is obtained by multiplying a flutter speed obtained by deterministic calculation by a safety coefficient, the safety coefficient is valued according to a margin K, uncertainty also exists in the safety coefficient, and a calculation equation of the uncertainty is as follows:

where VL represents the cumulative distribution function of the flutter boundaries;

the uncertainty calculation equation for the whole system is:

4.2 quantification of margin: the margin is the safe distance between the flutter boundary and the probability box distribution of the flutter speed, and the calculation equation is as follows:

4.3 solving a confidence factor for judging the safety of the flutter margin, wherein the calculation equation of the confidence factor is as follows:

in the QMU technology, when CR is larger than 1, the system is considered to be safe, the defined chattering boundary has enough margin to cover uncertainty, and the CR is used as a criterion for evaluating the safety of the chattering boundary.