主动学习基自适应PC⁃Kriging模型的复合材料结构可靠度算法

doi:10.7527/S1000-6893.2023.28982

Abstract

Abstract:

To address the complex， high dimensional， highly nonlinear， and long computing time-consuming problems of random natural frequency reliability analysis of composite wings， a reliability algorithm based on active learning basis-adaptive PC-Kriging model is proposed in this paper. A basis-adaptive strategy is used in this model to determine the orthogonal polynomial basis of the polynomial chaos expansion to approximate the global response of the numerical model， and Kriging is used for higher-order nonlinear interpolation to approximate the local response of the numerical model. In the framework of active learning reliability calculation， weighted K mean clustering is introduced， which means that K candidate sample points with greater contribution to failure probability are added in one iteration to reduce the number of iterations and accelerate the convergence rate. The effectiveness and accuracy of the proposed method are proved by a highly nonlinear numerical example. The proposed method is applied to the random natural frequency reliability analysis of composite plate and composite wing， and the accurate and efficient reliability calculation results are obtained.

Key words: reliability analysis, Basis-adaptive PC-Kriging, active learning, weighted K mean clustering, composite wings, random natural frequency

CLC Number:

V240.2

Yulian GONG, Jianguo ZHANG, Zhigang WU, Guangyuan CHU, Xiaoduo FAN, Ying HUANG. Reliability algorithm of composite structure based on active learning basis-adaptive PC-Kriging model[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 228982-228982.

Figures/Tables 15

Fig.1

Fig.2

Table 1

Comparison of reliability calculation results using different metamodels in a numerical example

方法	失效概率 $P ̂ f$ /10^-3	调用总次数 $N f$	误差 $ε P ̂ f / %$
MCS	4.713	1×10⁶
FORM	25.634	779	>100
SORM	3.671	791	22.54
ASVM	4.726	90	0.28
APCE	4.828	78	2.43
AKriging	4.712	54	0.02
APCK_Proposed	4.712	45	0.02

Table 1

Fig.3

Table 2

Distribution of random input variables of composite plate

变量	均值	标准差	分布类型
玻璃/环氧树脂密度 $ρ c$ /（kg·m^-3）	3.202×10⁴	3.202×10³	正态分布
11 方向弹性模量 $E 11$ /Pa	1.38×10¹¹	1.38×10¹⁰	正态分布
22 方向弹性模量 $E 22$ /Pa	8.9×10⁹	8.9×10⁸	正态分布
泊松比 $v$	0.3	0.03	正态分布
12 方向剪切模量 $G 12$ /Pa	7.1×10⁹	7.1×10⁸	正态分布
13 方向剪切模量 $G 13$ /Pa	7.1×10⁹	7.1×10⁸	正态分布
23 方向剪切模量 $G 23$ /Pa	2.84×10⁹	2.84×10⁸	正态分布
铺层厚度 $t$ /m	1.333×10^-3	1.333×10^-4	正态分布
45°铺层角 $A 1$ /（°）	45	4.5	正态分布
-45°铺层角 $A 2$ /（°）	45	4.5	正态分布
45°铺层角 $A 3$ /（°）	45	4.5	正态分布

Table 2

Fig.4

Table 3

Comparison of reliability calculation results using different metamodels in Case 1

方法	失效概率 $P ̂ f$ /10^-3	调用总次数 $N f$	误差 $ε P ̂ f / %$
MCS	3.400	1×10⁵
ASVM	3.209	83	5.63
APCE	3.456	49	1.65
AKriging	3.572	64	5.06
APCK_Proposed	3.406	64	0.16

Table 3

Fig.5

Fig.6

Fig.7

Table 4

Table 5

Distribution of random input variables of composite wing structure

变量	均值	标准差	分布类型
碳纤复合材料密度 $ρ c$ /（kg·m^-3）	1 780	178	正态分布
11 方向弹性模量 $E 11$ /Pa	5.5×10¹⁰	5.5×10⁹	正态分布
22 方向弹性模量 $E 22$ /Pa	5.5×10¹⁰	5.5×10⁹	正态分布
泊松比 $v$	0.04	0.004	正态分布
12 方向剪切模量 $G 12$ /Pa	4.3×10⁹	4.3×10⁸	正态分布
13 方向剪切模量 $G 13$ /Pa	1.0×10⁹	1.0×10⁸	正态分布
23 方向剪切模量 $G 23$ /Pa	1.0×10⁹	1.0×10⁸	正态分布
铺层厚度 $t$ /m	8×10^-3	8×10^-4	正态分布
30°铺层角 $B 1$ /（°）	30	4.5	正态分布
-30°铺层角 $B 2$ /（°）	30	4.5	正态分布
45°铺层角 $B 3$ /（°）	45	4.5	正态分布
-45°铺层角 $B 4$ /（°）	45	4.5	正态分布
45°铺层角 $B 5$ /（°）	45	4.5	正态分布
-45°铺层角 $B 6$ /（°）	45	4.5	正态分布

Table 5

Fig.8

Table 6

Comparison of reliability calculation results using different metamodels in Case 2

方法	失效概率 $P ̂ f$ /10^-3	调用总次数 $N f$	误差 $ε P ̂ f / %$
MCS	8.400	1×10⁵
ASVM	7.630	102	9.17
APCE	8.860	46	5.48
AKriging	9.040	76	7.62
APCK_Proposed	8.761	46	4.30

Table 6

Fig.9

References 22

1	龚煜廉，张建国，李文博. 光纤传感在航天复材结构健康监测中的应用［J］. 航天器工程， 2022， 31（5）： 60-66.
	GONG Y L， ZHANG J G， LI W B. Application of optical fiber sensing in health monitoring of aerospace composite structure［J］. Spacecraft Engineering， 2022， 31（5）： 60-66 （in Chinese）.
2	DEY S， MUKHOPADHYAY T， ADHIKARI S. Uncertainty quantification in laminated composites： A meta-model based approach［M］. London： CRC Press， 2017： 1-16.
3	晏良. 不确定性量化的代理模型分析及优化［D］. 长沙：国防科技大学， 2018： 7-11.
	YAN L. Analysis and optimization of agent model for uncertainty quantization［D］.Changsha： National University of Defense Technology， 2018： 7-11 （in Chinese） .
4	LEMAIRE M. Structural reliability［M］. Hoboken：John Wiley & Sons， 2013： 3.
5	SEPAHVAND K， SCHEFFLER M， MARBURG S. Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates： Analytical and experimental investigation［J］. Applied Acoustics， 2015， 87： 23-29.
6	DEY S， MUKHOPADHYAY T， SAHU S K， et al. Effect of cutout on stochastic natural frequency of composite curved panels［J］. Composites Part B： Engineering， 2016， 105（1）： 188-202.
7	DEY S， NASKAR S， MUKHOPADHYAY T， et al. Uncertain natural frequency analysis of composite plates including effect of noise - A polynomial neural network approach［J］. Composite Structures， 2016， 143（5）： 130-142.
8	MUKHOPADHYAY T， NASKAR S， KARSH P K， et al. Effect of delamination on the stochastic natural frequencies of composite laminates［J］. Composites Part B： Engineering， 2018， 154（7）： 242-256.
9	CHEN X， QIU Z P. A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables［J］. Composite Structures， 2018， 184（11）： 400-410.
10	ZHOU Y， ZHANG X F. Natural frequency analysis of functionally graded material beams with axially varying stochastic properties［J］. Applied Mathematical Modelling， 2019， 67（10）： 85-100.
11	ZHANG X， LIU Y， CAO X B， et al. Uncertain natural characteristics analysis of laminated composite plates considering geometric nonlinearity［J］. Composite Structures， 2023， 315（4）： 117028.
12	MARELLI S， SUDRET B. UQLab： A framework for uncertainty quantification in Matlab［C］∥ Vulnerability， Uncertainty， and Risk. Reston： American Society of Civil Engineers， 2014.
13	SCHOBI R， SUDRET B， WIART J. Polynomial-chaos-based kriging［J］. International Journal for Uncertainty Quantification， 2015， 5（2）： 171-193.
14	MOONEY C Z. Monte Carlo simulation［M］. Addison：Sage， 1997.
15	ECHARD B， GAYTON N， LEMAIRE M. AK-MCS： An active learning reliability method combining Kriging and Monte Carlo Simulation［J］. Structural Safety， 2011， 33（2）： 145-154.
16	ZAKI M J， MEIRA W. Data mining and analysis： Fundamental concepts and algorithms ［M］. New York： Cambridge University Press， 2014.
17	MOUSTAPHA M， MARELLI S， SUDRET B. UQLab user manual-active learning reliability： UQLab-V 2.0-117. Zurich： Chair of Risk， Safety and Uncertainty Quantification， 2022.
18	WANG J S， LI C F， XU G J， et al. Efficient structural reliability analysis based on adaptive Bayesian support vector regression［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 387（9）： 114172.
19	YI J X， ZHOU Q， CHENG Y S， et al. Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion［J］. Structural and Multidisciplinary Optimization， 2020， 62（5）： 2517-2536.
20	WU H， YAN Y， LIU Y J. Reliability based optimization of composite laminates for frequency constraint［J］. Chinese Journal of Aeronautics， 2008， 21（10）： 320-327.
21	FENG K X， LU Z Z， CHEN Z B， et al. An innovative Bayesian updating method for laminated composite structures under evidence uncertainty［J］. Composite Structures， 2023， 304（10）： 116429.
22	TOMBLIN J， MCKENNA J， NG Y， et al. Advanced general aviation transport experiments： Agate-wp3.3-033051-134 ［S］. Washington，D.C.：NASA， 2002.

阶数	频率/Hz
1	21.138
2	78.045
3	109.85

[1]	Fan ZHANG, Bohan CHENG, Peng WANG, Lei DONG. A two-stage degradation model and reliability analysis related to degradation of binary load-sharing systems [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(7): 229046-229046.
[2]	Fan ZHANG, Zijing SUN, Guosong XIAO, Jiachen LIU, Peng WANG. Reliability analysis for multi-phased mission of HUD system based on intuitionistic fuzzy Bayesian network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 226853-226853.
[3]	Lechang YANG, Chenxing WANG. Parameter calibration and reliability analysis of an aero-engine rotor based on multi-source heterogeneous information [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(23): 228575-228575.
[4]	Feng JIANG, Huacong LI, Jiangfeng FU, Linxiong HONG. A RBF and active learning combined method for structural non-probabilistic reliability analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 226667-226667.
[5]	Yunwen FENG, Xinyi LIN, Xiaofeng XUE, Xiang YANG, Jiaqi LIU. Design of civil aircraft explosion-proof structure for high reliable one-way blasting [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 228297-228297.
[6]	HE Yong, WANG Hong, LI Jing, QI Yankun. Joint decision making for condition-based maintenance and spare parts ordering of components based on vibration monitoring [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 225304-225304.
[7]	JIA Beixi, LYU Zhenzhou, LEI Jingyu. Parameterized simulation platform of turbine cooling film blade life reliability analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(12): 224747-224747.
[8]	HU Xiaoyi, WANG Ruping, WANG Xin, FU Yongtao. Recent development of safety and reliability analysis technology for model-based complex system [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(6): 523436-523436.
[9]	YOU Lingfei, ZHANG Jianguo, ZHOU Shuang, DU Xiaosong. A new method for fatigue reliability calculation of aero-engine limited life parts [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(12): 223228-223228.
[10]	LI Fang, HE Youchen, DI Peng, CHEN Tong, YIN Dongliang. Reliability analysis of fuzzy k-out-of-n system considering maintenance influence and dynamic load distribution mechanism [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(4): 221718-221718.
[11]	LIU Fuchao, WEI Pengfei, ZHOU Changcong, ZHANG Zheng, YUE Zhufeng. Time-dependent reliability and sensitivity analysis for planar motion mechanisms with revolution joint clearances [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(11): 422133-422141.
[12]	LI Yan, ZHANG Shuguang, GONG Qi. An improved probabilistic risk assessment method of structural parts for aeroengine [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(2): 597-608.
[13]	ZHANG Zhai, WANG Youren. Cell granularity optimization method of embryonics hardware in application design process [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(11): 3502-3511.
[14]	TONG Cao, SUN Zhili, YANG Li, SUN Anbang. An active learning reliability method based on Kriging and Monte Carlo [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 2992-3001.
[15]	LIU Chengwu, JIN Xiaoxiong, LIU Yunping, LIU Jihong. Reliability-based Multidisciplinary Design Optimization Integrating BLISCO and iPMA [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(11): 3054-3063.

Reliability algorithm of composite structure based on active learning basis-adaptive PC-Kriging model

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 15

References 22

Related Articles 15

Recommended Articles

Metrics

Comments