基于自适应Kriging的中介机匣结构可靠性分析

邸昊源; 李洪双

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

邸昊源,
李洪双^*, ,

南京航空航天大学飞行器先进设计技术国防重点学科实验室，南京 210016

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
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出版历程
- 收稿日期: 2022-09-19
- 网络出版日期: 2024-02-28

Reliability analysis of intermediate casing based on adaptive Kriging

DI Haoyuan,
LI Hongshuang^{*
, ,}

National Defense Key Laboratory of Aircraft Advanced Design Technology，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

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。
- 中介机匣 /
- 参数化建模 /
- Copula模型 /
- 自适应Kriging /
- 广义子集模拟
Abstract:
In order to explore the structural reliability analysis method of the intermediate casing under multiple failure modes, a parametric finite element model was established for the deterministic analysis of an aero-engine intermediate casing. Considering the uncertainty of material properties, geometric parameters and external loads of the aero-engine intermediate casing, the limit state functions were constructed for the two most typical failure modes of the intermediate casing: static strength failure and stiffness failure. By constructing an adaptive Kriging surrogate model for two failure modes and combining with the generalized subset simulation method, the failure probability of the intermediate casing structure was predicted. And the correlation of the two failure modes was modeled based on the Copula function theory to determine the mutual influence between them, and the calculation results were compared with AK-GSS method. The results showed that the failure probability of the intermediate casing structure system was in the order of $ {R_2} $. Compared with the conventional method, the computational time of the AK-GSS method for solving the failure probability was reduced by 87.7% almost without loss of computational accuracy. In addition, the AK-GSS method still had high accuracy when considering the correlation between the two failure modes of the intermediary magazine.
- intermediate casing /
- parametric modeling /
- Copula modeling /
- adaptive Kriging /
- generalized subset simulation

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图 1 中介机匣结构

Figure 1. Intermediate casing structure

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图 2 中介机匣有限元模型

Figure 2. Intermediate casing finite element model

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图 3 中介机匣Mises应力云图

Figure 3. Mises stress contour of intermediate casing

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图 4 中介机匣径向位移云图

Figure 4. Radial displacement contour of intermediate casing

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图 5 Python参数化建模流程

Figure 5. Parametric modeling process based on Python

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图 6 自适应Kriging模型构建流程

Figure 6. Establishment process of adaptive Kriging surrogate model

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图 7 刚度失效模式下结果对比图

Figure 7. Comparison of results in stiffness failure mode

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图 8 中介机匣Mises应力对比图

Figure 8. Comparison of Mises stress of intermediate casing

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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

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图 10 Copula模型建模流程

Figure 10. Modeling process of Copula model

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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/MPa	110000
许用应力/MPa	1123

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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

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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	E_RMS	R²	E_MR/%
Mises应力	4.6056	0.67	4.43
径向位移	0.1565	0.96	4.76

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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

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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

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