CN106599492B - A kind of the aircraft flutter analysis and its QMU appraisal procedure of logic-based recurrence - Google Patents

Abstract

A kind of the aircraft flutter analysis and its QMU appraisal procedure of logic-based recurrence, are related to nargin and uncertain quantification technique.The following steps are included: 1) establish the database of existing flight test, i.e., in the case where certain organizes design parameter, whether flight test occurs flutter, and flutter is denoted as 1, not flutter and is denoted as 0；2) regressive prediction model is established；3) it is fitted regression coefficient；4) prediction model；5) QMU is assessed.Complicated finite element analysis process is crossed, computational efficiency is high, and it is easy to operate, the neighborhood carried out is difficult to suitable for numerical simulations such as hypersonic heat structure flutters.Analysis result is assessed using QMU, while considering the uncertainty of flutter speed and Flutter Boundaries, the safety criterion as Flutter Problem is with a high credibility.The probability that flutter occurs for aircraft under the conditions of a certain design variable can be predicted, can be used for the design of assisting in flying device.

Description

A kind of the aircraft flutter analysis and its QMU appraisal procedure of logic-based recurrence

Technical field

The present invention relates to nargin and uncertain quantification technique, the aircraft returned more particularly, to a kind of logic-based quivers Vibration analysis and its QMU appraisal procedure.

Background technique

Flutter is a kind of aeroelasticity instability generated by the effect of intercoupling of air force, inertia force and elastic force Phenomenon.With the continuous promotion of contemporary aircraft speed, Flutter Problem also becomes to become increasingly conspicuous, the flutter analysis of Flight Vehicle Structure Cause the extensive concern of researcher.And in hypersonic aircraft field, severe pneumatic thermal environment makes flutter analysis It is encountered by new test, the important topic that hypersonic aircraft faces when flutter analysis of the structure under thermal environment.

Traditional aircraft Flutter Analysis Methods are will to test to combine with numerical simulation to analyze.But for number For value emulation, on the one hand due to the complexity of Aeroelastic Problems, there is very big uncertainties for the result emulated； COMPOSITE FINITE ELEMENT modeling method used by another aspect hypersonic aircraft is also immature, and finite element method is faced with Stern challenge.And flutter test has the characteristics that cost is high, the period is long.Therefore how according to limited test data come It is most important to accurate safe Flutter Boundaries.

Logistic regression is a kind of linear regression analysis model of broad sense, is usually used in data mining and economic forecasting field, together When can be used for finding the risk factor of certain event.Aircraft flutter is used for based on limited test flight data, by logistic regression Analysis can cross complicated simulation analysis process, analyze the Flutter Boundaries of aircraft well, and analysis result can be used for auxiliary Help Flight Vehicle Design.

QMU (quantification of margins and uncertainties, nargin and uncertain quantization skill 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 the factor (Confidence Factors) CF, i.e. performance margin M and not true foot U characterize performance margin and uncertain This relationship between property, as CF > 1, it is believed that system is safe.This method can be used as under condition of uncertainty, The safety evaluation foundation of flight structure flutter margin.

Summary of the invention

The purpose of the invention is to overcome deficiencies of the prior art, a kind of flying for logic-based recurrence is provided Row device flutter analysis and its QMU appraisal procedure.

The present invention the following steps are included:

1) database of existing flight test is established, i.e., whether flight test occurs flutter in the case where certain organizes design parameter, quivers Vibration is denoted as 1, not flutter and is denoted as 0；

2) regressive prediction model is established:

In formula (1), Y=1 indicates that flutter occurs, and flutter, Y do not occur for Y=0 expression^*It is implicit defined in logic returns to Variable

In formula (2), X_iIt is the design variable that can observe, ε indicates the uncertain error of model, β₀、β_iIt is unknown intend Collaboration number need to find out fitting coefficient using the method for maximal possibility estimation, be denoted as

Then the probability of generation flutter is under the design variable

F is the accumulated probability distribution function of ε in formula (4), is had for the Logic Regression Models of standard

F (η)=e^η/(1+e^η) (5)

By being distributed to becoming second nature it is found that the probability that flutter occurs is

P { Y=1 }=1-F (- η)=F (η) (6)

3) it is fitted regression coefficient:

It is illustrated by taking single design variable as an example, knows that regression model is by formula (2)

N is test data number in formula (7).Fitting coefficient β is found out using the method for maximal possibility estimation_i.

4) prediction model:

Under the conditions of certain design variable, the probability of aircraft flutter is

The anti-solution equation, can be obtained the value of the design variable under a certain flutter probability, designs for assisting in flying device

For Logic Regression Models, take p=0.5 as Flutter Boundaries, p=0.05 is flutter threshold value, while can be analyzed 95% confidence interval of Flutter Boundaries and threshold value out.

5) QMU is assessed:

To a certain design variable x, the probability of aircraft flutter under this condition is analyzed using regression analysis software p_flutter, while providing its 95% confidence interval [p_{flutter,lower},p_{flutter,upper}], and then regression curve is combined, it obtains and sets Count 95% confidence interval of variable xTaking design variable corresponding to p=0.5 is flutter side Boundary x_flutter, can similarly obtain x_flutter95% confidence intervalIt takes and is set corresponding to p=0.05 Meter variable is flutter threshold value x_gate, can similarly obtain x_gate95% confidence interval

Then flutter margin M:

M=x_fluter-x_gate (10)

Uncertain U is by Flutter Boundaries uncertainty U_flutterWith flutter threshold value uncertainty U_gateTwo parts composition:

To obtain confidence factor

The present invention, using limited test flight data, passes through logistic regression in the case where numerical simulation is difficult to be unfolded Analysis method analyzes aircraft Flutter Boundaries, while can provide aircraft and design variable required by flutter does not occur Value range is designed for assisting in flying device, is finally assessed using QMU appraisal procedure analysis result.

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

1) logic-based returns and limited test data analyzes aircraft flutter, has crossed complicated finite element Analytic process, computational efficiency is high, easy to operate, is difficult to the neighbour carried out suitable for numerical simulations such as hypersonic heat structure flutters Domain.

2) analysis result is assessed using QMU, while considers the uncertainty of flutter speed and Flutter Boundaries, as The safety criterion of Flutter Problem is with a high credibility.

3) probability that flutter occurs for aircraft under the conditions of a certain design variable can be predicted, can be used for assisting in flying device and set Meter.

Detailed description of the invention

Fig. 1 is prediction model of the logistic regression analysis to Flutter Boundaries.

Fig. 2 is Flutter Boundaries and flutter threshold value and its 95% confidence interval schematic diagram.

Fig. 3 is the nargin M and uncertainty U schematic diagram of QMU analysis.

Specific embodiment

Take below flying speed as unitary variant for, aircraft flutter is analyzed (if examining using logistic regression Consider other design variables, then can obtain the value range of variable when flutter does not occur for aircraft), specific implementation step includes:

1, the input of experimental data is realized using matlab logistic regression tool box, and is fitted the recurrence for obtaining logistic regression Factor beta_i.The test flight data of certain model aircraft is as shown in table 1.

2, linear logic regression fit is carried out using glmfit and glmval function in Matlab, obtaining regression coefficient isThen aircraft flutter anticipation function is

The test flight data of certain the model aircraft of table 1

Prediction model functional image using matlab as shown in Figure 1, also draw point of 95% confidence interval of p (x) simultaneously Cloth.Soft dot indicates that test data point, solid line represent logistic regression anticipation function in figure, and dotted line is its 95% confidence interval Distribution function.

3, flutter probability value p (x)=0.5 is taken, can obtain the aircraft flutter speed analyzed under this condition

And mode obtains the confidence interval [V of flutter speed 95% according to Fig.2,_{flutter,lower},V_{flutter,upper}]。

The flutter speed for taking 5% Probability Point is flutter threshold value V_gate=V (p=0.05), 95% confidence interval are [V_gate,lower,V_gate,upper], it is believed that aircraft is less than threshold value V in flying speed_gateFlutter occurs for Shi Buhui.

It is as follows to analyze result QMU assessment specific implementation process:

1, the uncertain U and nargin M of flutter speed threshold value and Flutter Boundaries are calculated according to formula (10) and (11).

2, confidence factor is calculated

If confidence factor is greater than 1.0, illustrate to analyze credible result to aircraft Flutter Boundaries by logistic regression analysis, Aircraft is less than threshold value V in flying speed under this design condition_gateFlutter occurs for Shi Buhui.

The nargin M and uncertainty U schematic diagram of QMU analysis are referring to Fig. 3.

Claims (1)

1. aircraft flutter analysis and its QMU appraisal procedure that a kind of logic-based returns, it is characterised in that the following steps are included:

1) regressive prediction model is established:

In formula (1), Y=1 indicates that flutter occurs, and flutter, Y do not occur for Y=0 expression^*It is implicit variable defined in logistic regression:

Y^*=β₀+β₁x+ε (2)

In formula (2), x is design variable, and ε indicates the uncertain error of model, β₀And β₁It is unknown fitting coefficient, according to Some test flight datas are acquired using the method for maximal possibility estimation；

2) model based on step 1) is predicted:

Remember η=β₀+β₁The probability of flutter then occurs at design variable x for x are as follows:

F is the cumulative distribution function of ε in formula (3), is had for the Logic Regression Models of standard:

F (η)=e^η/(1+e^η) (4)

By the symmetry that is distributed it is found that the probability of flutter occurs are as follows:

P { Y=1 }=1-F (- η)=F (η) (5)

Inverse equation (5), obtains the value of design variable x under flutter probability P, designs for assisting in flying device；

3) QMU is assessed:

Taking design variable corresponding to P=0.5 is Flutter Boundaries x_flutter, and provide x_flutter95% confidence intervalSeparately taking design variable corresponding to P=0.05 is flutter threshold value x_gate, and provide x_gate95% confidence interval

Then flutter margin M:

M=x_flutter-x_gate (7)

Uncertain U is by Flutter Boundaries uncertainty U_flutterWith flutter threshold value uncertainty U_gateTwo parts composition:

To obtain confidence factor