基于Kriging模型梯度解析解的改进一次二阶矩方法

doi:10.7527/S1000-6893.2018.22629

Abstract

Abstract: The Advanced First Order and Second Moment (AFOSM) method is a structural reliability analysis method based on the gradient information of performance function. Since the gradient information of the implicit function is difficult to solve, an AFOSM method based on the gradient analytical solution of Kriging surrogate model is proposed, using the analytical expression of Kriging surrogate model to obtain gradient information of the performance function with respect to input variables, and providing a high-precision gradient information for the computation of the design point in the AFOSM method. By combining Kriging and AFOSM, the problem of gradient calculation and reliability analysis in the implicit situation based on the finite element model can be better solved. Numerical and engineering examples are introduced to verify the high precision of the proposed gradient solution based on Kriging; besides, the accuracy and precision of the proposed Kriging analytical solution based AFOSM reliability analysis method are also verified.

Key words: structural reliability, Kriging surrogate model, gradient analytical solution, advanced first order and second moment, probability density

CLC Number:

V19
TB114.3

LI Baoyu, ZHANG Leigang, QIU Qunhai, YU Xiongqing. An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 222629-222629.

References

[1] THOFT-CHRISTENSEN P, MUROTSU Y. Application of structural systems reliability theory[M]. Berlin:Springer-Verlag, 1986.
[2] HASOFER A M, LIND N C. An exact and invariant first order reliability format[J]. Journal of Engineering Mechanics, 1974, 100(1):111-121.
[3] 吕震宙, 宋述芳, 李洪双, 等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京:科学出版社, 2009. LU Z Z, SONG S F, LI H S, et al. Reliability and reliability sensitivity analysis of structure and mechanism[M]. Beijing:Science Press, 2009(in Chinese).
[4] SACKS J, SCHILLER S B, WELCH W J. Design for computer experiment[J]. Technometrics, 1989, 31(1):41-47.
[5] 张磊刚. 不确定性结构的局部和矩独立灵敏度方法研究[D]. 西安:西北工业大学, 2015. ZHANG L G. Research on local and moment-independent sensitivity analysis for structures with uncertainty[D].Xi'an:Northwestern Polytechnical University, 2015(in Chinese).
[6] SIMPSON T W, MAUERY T M, KORTE J J, et al. Comparison of response surface and kriging models for multidisciplinary design optimization:AIAA-1998-4755[R]:Reston, VA:AIAA, 1998.
[7] SAKATA S, ASHIDA F, ZAKO M. Structural optimization using kriging approximation[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(7-8):923-939.
[8] LUCIFREDI A, MAZZIERI C, ROSSI M. Application of multi-regressive linear models, dynamic kriging models and neural network models to predictive maintenance of hydroelectric power systems[J]. Mechanical Systems and Signal Processing, 2000, 14(3):471-494.
[9] ZHANG L, LU Z, WANG P. Efficient structural reliability analysis method based on advanced Kriging model[J]. Applied Mathematical Modelling, 2015, 39(2):781-793.
[10] CHEN W, RUICHEN J, AGUS S. Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty[J]. Journal of Mechanical Design, 2005, 127(5):875-886.
[11] ZHANG L, LU Z, CHENG L, el al. Emulator model based analytical solution for reliability sensitivity analysis[J]. Journal of Engineering Mechanics, ASCE, 2015, 141(8):04015016.
[12] RACKWITZ R, FIESSLER B. Structural reliability under combined random load sequences[J]. Computers and Structures, 1978, 9(5):489-494.
[13] OLSSON A, SANDBERG G, DAHLBLOM D. On Latin hypercube sampling for structural reliability analysis[J]. Structural Safety, 2003, 25(1):47-68.
[14] 张磊刚, 吕震宙, 陈军. 基于失效概率的矩独立重要性测度的高效算法[J]. 航空学报, 2014, 35(8):2199-2206. ZHANG L G, LU Z Z, CHEN J. An efficient method for failure probability-based moment-independent importance measure[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(8):2199-2206(in Chinese).
[15] 罗阳军, 高宗战, 岳珠峰, 等. 随机有界混合不确定性下结构可靠性优化设计[J]. 航空学报, 2011, 32(6):1058-1066. LUO Y J, GAO Z Z, YUE Z F, et al. Reliability-based optimization design for structures with stochastic and bounded parameter uncertainties[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(6):1058-1066(in Chinese).
[16] 赵海龙, 岳珠峰, 刘伟. 矩独立重要性分析的Kriging代理模型方法[J]. 航空学报, 2016, 37(7):2234-2241. ZHAO H L, YUE Z F, LIU W. A Kriging surrogate model method for moment-independent importance analysis[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(7):2234-2241(in Chinese).

An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Hongwei QIAO, Jianhan LIANG, Lin ZHANG, Mingbo SUN, Yuqiao CHEN. Research progress of probability density function approach in supersonic combustion [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 28802-028802.
[2]	Qingdi GUAN, Jianhan LIANG, Lin ZHANG, Wenwu CHEN, Yuqiao CHEN. Probability density function method in general curvilinear coordinate system and its application in supersonic combustion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 126677-126677.
[3]	Ting YU, Luyi LI, Yushan LIU, Zeming CHANG. Efficient Bayesian updating method under observation uncertainty and its application in wing structure [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(24): 228592-228592.
[4]	Ying ZHANG, Xiaoying LI, Jianan YIN, Xiaotong ZHOU. Flexible control of aircraft departure pushback time based on probabilistic taxiing time [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(10): 327452-327452.
[5]	CHEN Zhiyuan, LI Luyi. Efficient methods for reliability sensitivity analysis of inputs with distribution parameter uncertainty [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 325881-325881.
[6]	WANG Fang, WANG Yudong, JIANG Shengli, CHEN Jun, TANG Jun, XU Huasheng, LI Xiangyuan, XING Jingwen, GAO Dongshuo, JIN Jie. Development and testing of AECSC-JASMIN turbulent combustion simulation software [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(12): 625003-625003.
[7]	SUN Dong, LIU Pengxin, TONG Fulin. Effect of spanwise oscillation on interaction of shock wave and turbulent boundary layer [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(12): 124054-124054.
[8]	TONG Fulin, ZHOU Guiyu, ZHOU Hao, ZHANG Peihong, LI Xinliang. Statistical characteristics of wall shear stress in shock wave and turbulent boundary layer interactions [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 122504-122504.
[9]	LI Lei, XIE Li, ZHANG Yongjie, WU Qin. Application of data mining in intelligence test of launch vehicles [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(S1): 722203-722203.
[10]	YANG Yin, SHENG Weixing, HAN Yubing, MA Xiaofeng. Shaped-beam pattern synthesis based on quantization of element excitation amplitude [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(4): 321653-321653.
[11]	YANG Yue, YOU Jiaping, SUN Mingbo. Modeling of turbulence-chemistry interactions in numerical simulations of supersonic combustion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(1): 261-273.
[12]	CHEN Shichun, HUANG Peilin, JI Jinzu. Radar Cross Section Fluctuation Characteristics of Typical Stealth Aircraft [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(12): 3304-3314.
[13]	XU Jiakuan, BAI Junqiang, HUANG Jiangtao, QIAO Lei, DONG Jianhong, LEI Wutao. Aerodynamic Optimization Design of Wing Under the Interaction of Propeller Slipstream [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(11): 2910-2920.
[14]	LV Zhaoyan, LV Zhenzhou, LI Guijie, TANG Zhangchun. Reliability Sensitivity Analysis Method Based on Weight Index of Density [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(1): 179-186.
[15]	FANG Guancheng, LU Zhenzhou, WEI Pengfei. Modified Subset Simulation Method for Reliability and Reliability Sensitivity Analysis of Structural System [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, 33(8): 1440-1447.