CN107633118A - Wing structure Parameter Sensitivity Analysis method based on random interval mixed model - Google Patents

Wing structure Parameter Sensitivity Analysis method based on random interval mixed model Download PDF

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CN107633118A
CN107633118A CN201710747451.5A CN201710747451A CN107633118A CN 107633118 A CN107633118 A CN 107633118A CN 201710747451 A CN201710747451 A CN 201710747451A CN 107633118 A CN107633118 A CN 107633118A
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mrow
msub
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munderover
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张峰
谭世旺
岳珠峰
高洋
王亚萌
敖良波
骆凯亮
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Northwestern Polytechnical University
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Abstract

The invention provides a kind of wing structure Parameter Sensitivity Analysis method based on random interval mixed model, it is related to aircraft reliability design field, the present invention proposes a kind of Parameter Sensitivity Analysis method under random interval mixed model, solution form of the wing box section power function for structural parameters sensitivity in the case of linear is derived, the present invention is with the box section structure sensitivity analysis of wing three, demonstrate the validity of analytic method, fail-safe analysis and structure of the analysis result of the present invention to wing box section, which change design, to have great significance, and it can derive in the Parameter Sensitivity Analysis of other labyrinths, such as aircraft door structure, aircraft flap structure etc..

Description

Wing structure Parameter Sensitivity Analysis method based on random interval mixed model
Technical field
The present invention relates to aircraft reliability design field, especially a kind of analysis method of sensitivity.
Background technology
One of the important component of wing as aircraft, its main function are to provide lift for aircraft and meet aircraft each Performance requirement under state of flight.Wing box is the main load part of wing, bears caused all load on wing.So wing Box structure design, the influence to the even whole aircraft of wing have vital effect.Good structure design can not only protect Demonstrate,prove wing and produce normal aerodynamic lift, and in wing system normal operation, and the performance of material can be given full play to Advantage, mitigate construction weight, improve structural reliability.
STRUCTURAL SENSITIVITY ANALYSIS INDESIGN is an importance of reliability design work, can be with from the result of sensitivity analysis Important reliability design factor is held, grasps the emphasis of the work such as design, processing and manufacturing, statistical reliability data, improves work Effect；Unessential reliability design factor can be simplified, these uncertain factors are handled as constant, so as to improve Reliability design efficiency.At present, it is increasingly ripe based on the structural parameters sensitivity analysis under probabilistic model.Based on probabilistic model Structural parameters sensitivity analysis needs to assert that parameter is stochastic variable, and has the information such as the regularity of distribution, average, variance of parameter, And during labyrinth reliability design, lack abundance information come determine the regularity of distribution of parameter of structure design, average, The information such as variance, probability density function, limit the application of the Parameter Sensitivity Analysis method based on probabilistic model.
Non-probability model can efficiently solve that data volume is less, the inferior reliability of variable probability density function deletion condition is asked Inscribe and receive much concern.Non-probability model describes to input uncertain factor using section domain, according to the computation model established Obtain output response uncertain excursion, this process do not need input parameter probability density function, solve with STRUCTURAL SENSITIVITY ANALYSIS INDESIGN problem of the machine variable in the case of parametric statistics poor in information.But interval variable is provided experimental data Information utilization is very low, although just with experimental data boundary information and it is equally distributed it is assumed that calculate it is simple, Its result of calculation is generally quite conservative.
Therefore, stochastic variable, interval variable are blended, establish labyrinth it is random-the structure ginseng of section mixed model Number Sensitivity Analysis and method for solving, join to solve structure in the case of aircraft complex structure division parametric statistics poor in information Several importance analysis degree problems, this is to this kind of high reliability product of aviation wing box section under Uncertain environments Performance prediction and optimization design plays directive function.
The content of the invention
For overcome the deficiencies in the prior art, the present invention does not fill for aircraft wing box section structure part design parameter information The situation of foot, a kind of Parameter Sensitivity Analysis method under random-section mixed model is proposed, has derived wing box section work( Can function for structural parameters sensitivity in the case of linear solution form.
The detailed step of the technical solution adopted for the present invention to solve the technical problems is as follows：
Step 1, the power function of aircraft wing box section structure is set as g (x, y), wherein x is structural parameters, is a m dimension Normal random vector, be designated as x=(x1,x2,…,xi,…,xm), xiFor i-th of structural parameters, its probability density function fi (xi) be：
Wherein, μiFor stochastic variable xiAverage, σiFor stochastic variable xiStandard deviation；
Y in formula (1) is structural parameters, is the interval vector of a n dimension, is designated as y=(y1,y2,…,yj,…,yn), yjFor j-th of structural parameters, the expression form of its uncertain feature is：
Wherein,For interval variable yjIntermediate value,For interval variable yjDeviation；
Step 2, when the power function g (x, y) of aircraft wing box section structure is linear function, be shown below：
xiFor separate normal random variable, yjFor separate interval variable；
When x takes a certain value in power function g (x, y) in step 3, formula (3), the non-probability of aircraft wing box section structure Reliability index η (x) is：
Wherein, η (x) is Multidisciplinary systems index when structural parameters x is fixed value；
Establish secondary function equation M(2)(x,y)
The mixing reliability index β that structure can be obtained is：
Variant structural parametric sensitivity under step 4, random-interval model is defined as mixing reliability index β to mixing The partial derivative of the distributed constant of variable (x, y), that is, mix mean μs of the reliability index β to hybrid variable (x, y)i, standard deviation sigmai、 Intermediate valueAnd deviationPartial derivative, its expression is as follows：
In formula (7), (8), (9) and (10)As variant structural parametric sensitivity.
The beneficial effects of the present invention are due to defining the sensitive of the wing box section parameter under random-interval model Index is spent, the Analytical Solution method that wing box section power function is parametric sensitivity under linear case is derived, with wing three Box section structure sensitivity analysis, it was demonstrated that the validity of analytic method, analysis result of the invention can to wing box section Change design by property analysis and structure and have great significance, and the Parameter Sensitivity Analysis of other labyrinths can be derived In, such as aircraft door structure, aircraft flap structure.
Brief description of the drawings
Fig. 1 is the box section structure figure of wing three of the present invention.
Embodiment
The present invention is further described with reference to the accompanying drawings and examples.
Certain box structure of aircraft wing three of the present embodiment, its structure are as shown in Figure 1.
Step 1, the power function of aircraft wing box section structure is set as g (x, y), wherein x is structural parameters, is a m dimension Normal random vector, be designated as x=(x1,x2,…,xi,…,xm), xiFor i-th of structural parameters, its probability density function fi (xi) be：
Wherein, μiFor stochastic variable xiAverage, σiFor stochastic variable xiStandard deviation；
Y in formula (1) is structural parameters, is the interval vector of a n dimension, is designated as y=(y1,y2,…,yj,…,yn), yjFor j-th of structural parameters, the expression form of its uncertain feature is：
Wherein,For interval variable yjIntermediate value,For interval variable yjDeviation；
Step 2, when the power function g (x, y) of aircraft wing box section structure is linear function, be shown below：
xiFor separate normal random variable, yjFor separate interval variable；
When x takes a certain value in power function g (x, y) in step 3, formula (3), the non-probability of aircraft wing box section structure Reliability index η (x) is：
Wherein, η (x) is Multidisciplinary systems index when structural parameters x is fixed value；
Establish secondary function equation M(2)(x,y)
The mixing reliability index β that structure can be obtained is：
Variant structural parametric sensitivity under step 4, random-interval model is defined as mixing reliability index β to mixing The partial derivative of the distributed constant of variable (x, y), that is, mix mean μs of the reliability index β to hybrid variable (x, y)i, standard deviation sigmai、 Intermediate valueAnd deviationPartial derivative, its expression is as follows：
In formula (7), (8), (9) and (10)As variant structural parametric sensitivity.
Shown in Fig. 1 for the box section structure of aircraft wing three, structure material is aluminium alloy, the intensity of construction unit (x1,x2) and the load (y that is applied1) it is variable.The dominant failure mode of structural system is obtained with optiaml ciriterion method, and Carry out variable (x1,x2,y1) unit normalized, the power function g (x, y) finally given is shown below：
G (x, y)=8.0x1+8.0x2-y1 (11)
In the present example, m=2, n=1 are taken；
(x1,x2) it is separate normal random variable, its parameter is as shown in table 1：
Table 1 is random-interval model in stochastic variable essential characteristic value
y1It is as shown in table 2 for interval variable, its parameter：
Table 2 is random-interval model in interval variable essential characteristic value
The result that the box section structure parametric sensitivity of wing three based on random-interval model calculates is as shown in table 3：
The box section structure Parameter Sensitivity Analysis result of 3 wing of table three
The present embodiment analyzes the parametric sensitivity of the box section structure of aircraft wing three, as a result as shown in table 3, structure ginseng Number x1、x2Standard deviation sigma1、σ2Influence bigger on mixing reliability index, it is necessary to be paid close attention in reliability design, so as to Direct structural reliability design.

Claims (1)

  1. A kind of 1. wing structure Parameter Sensitivity Analysis method based on random interval mixed model, it is characterised in that including following Step：
    Step 1, set the power function of aircraft wing box section structure as g (x, y), wherein x is structural parameters, be a m dimension just State random vector, it is designated as x=(x1,x2,…,xi,…,xm), xiFor i-th of structural parameters, its probability density function fi(xi) be：
    <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mi>exp</mi> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mi>i</mi> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, μiFor stochastic variable xiAverage, σiFor stochastic variable xiStandard deviation；
    Y in formula (1) is structural parameters, is the interval vector of a n dimension, is designated as y=(y1,y2,…,yj,…,yn), yjFor J-th of structural parameters, the expression form of its uncertain feature are：
    <mrow> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,For interval variable yjIntermediate value,For interval variable yjDeviation；
    Step 2, when the power function g (x, y) of aircraft wing box section structure is linear function, be shown below：
    <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>b</mi> <mi>j</mi> </msub> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    xiFor separate normal random variable, yjFor separate interval variable；
    When x takes a certain value in power function g (x, y) in step 3, formula (3), the non-probability decision of aircraft wing box section structure Property index η (x) is：
    <mrow> <mi>&amp;eta;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>b</mi> <mi>j</mi> </msub> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, η (x) is Multidisciplinary systems index when structural parameters x is fixed value；
    Establish secondary function equation M(2)(x,y)
    <mrow> <msup> <mi>M</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&amp;eta;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    The mixing reliability index β that structure can be obtained is：
    <mrow> <mi>&amp;beta;</mi> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>&amp;mu;</mi> <mi>i</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Variant structural parametric sensitivity under step 4, random-interval model is defined as mixing reliability index β to hybrid variable The partial derivative of the distributed constant of (x, y), that is, mix mean μs of the reliability index β to hybrid variable (x, y)i, standard deviation sigmai, intermediate valueAnd deviationPartial derivative, its expression is as follows：
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;beta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;mu;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>a</mi> <mi>i</mi> </msub> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <msub> <mi>X</mi> <mi>i</mi> </msub> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;beta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mo>&amp;lsqb;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>&amp;mu;</mi> <mi>i</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <msup> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;beta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>c</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mi>j</mi> </msub> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;beta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>r</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mo>|</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    In formula (7), (8), (9) and (10)As variant structural parametric sensitivity.
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CN108763611A (en) * 2018-03-28 2018-11-06 北京航空航天大学 A kind of wing structure random eigenvalue analysis method based on probabilistic density evolution
CN108763611B (en) * 2018-03-28 2022-03-15 北京航空航天大学 Wing structure random eigenvalue analysis method based on probability density evolution
CN110941881A (en) * 2019-10-16 2020-03-31 北京航空航天大学 Mixed uncertainty structure fatigue life analysis method based on chaos polynomial expansion
CN113051851A (en) * 2021-04-19 2021-06-29 电子科技大学 Sensitivity analysis method under mixed uncertainty

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