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基于自适应Kriging的中介机匣结构可靠性分析

邸昊源 李洪双

邸昊源, 李洪双. 基于自适应Kriging的中介机匣结构可靠性分析[J]. 航空动力学报, 2024, 39(9):20220707 doi: 10.13224/j.cnki.jasp.20220707
引用本文: 邸昊源, 李洪双. 基于自适应Kriging的中介机匣结构可靠性分析[J]. 航空动力学报, 2024, 39(9):20220707 doi: 10.13224/j.cnki.jasp.20220707
DI Haoyuan, LI Hongshuang. Reliability analysis of intermediate casing based on adaptive Kriging[J]. Journal of Aerospace Power, 2024, 39(9):20220707 doi: 10.13224/j.cnki.jasp.20220707
Citation: DI Haoyuan, LI Hongshuang. Reliability analysis of intermediate casing based on adaptive Kriging[J]. Journal of Aerospace Power, 2024, 39(9):20220707 doi: 10.13224/j.cnki.jasp.20220707

基于自适应Kriging的中介机匣结构可靠性分析

doi: 10.13224/j.cnki.jasp.20220707
基金项目: 江苏高校优势学科建设工程资助
详细信息
    作者简介:

    邸昊源(1998-),男,博士生,主要从事结构可靠性设计研究。E-mail:dihy516@nuaa.edu.cn

    通讯作者:

    李洪双(1978-),男,教授,博士,主要从事飞行器结构可靠性设计研究。E-mail:hongshuangli@nuaa.edu.cn

  • 中图分类号: V232.6

Reliability analysis of intermediate casing based on adaptive Kriging

  • 摘要:

    为了探究中介机匣在多失效模式下的结构可靠性分析方法,建立了参数化有限元模型进行确定性分析。考虑航空发动机中介机匣的材料性能、几何参数及外部载荷的不确定性,对中介机匣两种最典型失效模式:静强度失效以及刚度失效建立极限状态函数。通过构造两失效模式下的自适应Kriging(adaptive Kriging,AK)模型并结合广义子集模拟(generalized subset simulation,GSS)方法评估中介机匣结构失效概率,并基于Copula函数理论对中介机匣失效模式的相关性进行建模,明确两失效模式之间的相互影响,并与AK-GSS方法计算结果进行对比。结果表明:中介机匣结构系统失效概率在10−6量级;相较于传统方法,AK-GSS方法求解中介机匣结构失效概率时计算时长缩减了87.7%且几乎未损失计算精度。除此之外,考虑中介机匣两失效模式相关时AK-GSS方法依旧具有高精度。

     

  • 图 1  中介机匣结构

    Figure 1.  Intermediate casing structure

    图 2  中介机匣有限元模型

    Figure 2.  Intermediate casing finite element model

    图 3  中介机匣Mises应力云图

    Figure 3.  Mises stress contour of intermediate casing

    图 4  中介机匣径向位移云图

    Figure 4.  Radial displacement contour of intermediate casing

    图 5  Python参数化建模流程

    Figure 5.  Parametric modeling process based on Python

    图 6  自适应Kriging模型构建流程

    Figure 6.  Establishment process of adaptive Kriging surrogate model

    图 7  刚度失效模式下结果对比图

    Figure 7.  Comparison of results in stiffness failure mode

    图 8  中介机匣Mises应力对比图

    Figure 8.  Comparison of Mises stress of intermediate casing

    图 9  两失效模式极限状态函数散点密度图

    Figure 9.  Scatter diagram of limit state function in two failure modes

    图 10  Copula模型建模流程

    Figure 10.  Modeling process of Copula model

    表  1  TC4材料参数

    Table  1.   TC4 material parameters

    参数数值及说明
    材料TC4
    密度/(g/cm³)4.51
    泊松比0.34
    弹性模量/MPa110000
    许用应力/MPa1123
    下载: 导出CSV

    表  2  中介机匣输入参数

    Table  2.   Intermediate casing input parameters

    序号 参数名称 分布 均值 变异系数 截断区间
    1 外机匣半径$ {R_1} $/mm 截断正态 200 0.02 [172, 288]
    2 内机匣半径$ {R_2} $/mm 截断正态 120 0.02 [103.2, 136.8]
    3 外机匣长度$ {L_1} $/mm 截断正态 100 0.02 [86, 114]
    4 内机匣长度$ {L_2} $/mm 截断正态 110 0.02 [94.6, 125.4]
    5 发动机推力$ F $/kN 正态分布 150 0.05
    6 弹性模量$ E $/MPa 正态分布 110000 0.03
    7 泊松比$ \mu $ 正态分布 0.34 0.03
    下载: 导出CSV

    表  3  自适应Kriging代理模型预测精度

    Table  3.   Prediction accuracy of AK surrogate model

    评估指标 ERMS R2 EMR/%
    Mises应力 4.6056 0.67 4.43
    径向位移 0.1565 0.96 4.76
    下载: 导出CSV

    表  4  两方法计算结果对比

    Table  4.   Comparison of calculation results of two methods

    方法 静强度失效
    概率/10−6
    刚度失效
    概率/10−6
    系统失效
    概率/10−6
    计算
    时长/s
    AK-GSS 2.0648 1.2308 3.0395 522.7
    AK-MCS 2.2000 1.2000 3.0000 4249.5
    下载: 导出CSV

    表  5  双失效模式的相关性模型

    Table  5.   Copula model of two failure modes

    求解
    参数
    Gaussian
    模型
    Clayton
    模型
    Gumbel
    模型
    Frank
    模型
    $\hat \theta $ 0.8966 1.8329 1.9633 5.8548
    AIC −33.1803 −32.5998 −29.5695 −29.3299
    ${d^2}$ 0.0208 0.0290 0.0245 0.0315
    下载: 导出CSV
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  • 收稿日期:  2022-09-19
  • 网络出版日期:  2024-02-28

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