Reliability analysis of structures using polynomial chaos expansions

ZHANG Ming; WANG Enzhi; LIU Yaoru; QI Wenbiao; WANG Dehui

doi:10.16511/j.cnki.qhdxxb.2022.25.015

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Journal of Tsinghua University(Science and Technology) ›› 2022, Vol. 62 ›› Issue (8) : 1314-1320. DOI: 10.16511/j.cnki.qhdxxb.2022.25.015

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Reliability analysis of structures using polynomial chaos expansions

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Abstract

Practical engineering issues such as design optimization, design space exploration, sensitivity analyses, and reliability analyses need many simulations. If a single simulation is very time-consuming, engineers cannot perform the thousands or even millions of simulations needed for such analyses. The polynomial chaos expansion (PCE) method is an effective method that allows analyses of complex problems. This paper introduces the mathematical theory of the PCE method and presents a structural reliability analysis example. The performance response function for the structural reliability analysis is expressed as a PCE using Hermite polynomials. A general form of the Hermite polynomial, which is suitable for use in a computer program, is used to generalize the PCE analysis program and the adaptive selection of the polynomial order. Then, the accuracy and applicability of the surrogate model are verified using structural reliability analysis examples with explicit performance functions. The results show that the model has an excellent convergence rate with higher order PCE giving higher accuracy. The examples also show that the direct use of explicit performance functions is the easiest way to investigate PCE surrogate models.

Key words

optimal design / structural reliability / polynomial chaos expansion (PCE) / Hermite polynomial / performance function

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ZHANG Ming, WANG Enzhi, LIU Yaoru, QI Wenbiao, WANG Dehui. Reliability analysis of structures using polynomial chaos expansions[J]. Journal of Tsinghua University(Science and Technology). 2022, 62(8): 1314-1320 https://doi.org/10.16511/j.cnki.qhdxxb.2022.25.015

References

[1] CHOI S K, GRANDHI R V, CANFIELD R A. Reliability-based structural design[M]. London:Springer, 2007.
[2] 侯少康, 刘耀儒. 双护盾TBM掘进数值仿真及护盾卡机控制因素影响分析[J]. 清华大学学报(自然科学版), 2021, 61(8):809-817. HOU S K, LIU Y R. Numerical simulations of double-shield TBM tunneling for analyzing shield jamming control factors[J]. Journal of Tsinghua University (Science and Technology), 2021, 61(8):809-817. (in Chinese)
[3] 熊芬芬, 杨树兴, 刘宇, 等. 工程概率不确定性分析方法[M]. 北京:科学出版社, 2015. XIONG F F, YANG S X, LIU Y, et al. Probabilistic uncertainty analysis methods for engineering problems[M]. Beijing:Science Press, 2015. (in Chinese)
[4] 张明, 金峰. 结构可靠度计算[M]. 北京:科学出版社, 2015. ZHANG M, JIN F. Structural reliability computations[M]. Beijing:Science Press, 2015. (in Chinese)
[5] 赵威. 结构可靠度分析代理模型方法研究[D]. 哈尔滨:哈尔滨工业大学, 2012. ZHAO W. Study on surrogate model methods for structural reliability analysis[D]. Harbin:Harbin Institute of Technology, 2012. (in Chinese)
[6] BAROTH J, SCHOEFS F, BREYSSE D. Construction reliability:Safety, variability and sustainability[M]. Hoboken:John Wiley & Sons, 2013.
[7] PETTERSSON M P, IACCARINO G, NORDSTRÖM J. Polynomial chaos methods for hyperbolic partial differential equations[M]. Cham:Springer, 2015.
[8] PELLEGRINI G. Polynomial chaos expansion with applications to PDEs[D]. Verona:University of Verona, 2013.
[9] XU J, WANG D. Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique[J]. Reliability Engineering & System Safety, 2019, 185:329-340.
[10] YU H, GILLOT F, ICHCHOU M. A polynomial chaos expansion based reliability method for linear random structures[J]. Advances in Structural Engineering, 2012, 15(12):2097-2111.
[11] HAWCHAR L, EL SOUEIDY C P, SCHOEFS F. Time-variant reliability analysis using polynomial chaos expansion[C]//12th International Conference on Applications of Statistics and Probability in Civil Engineering. Vancouver, Canada:ICASP, 2015.
[12] CLARICH A, MARCHI M, RIGONI E, et al. Reliability-based design optimization applying polynomialchaos expansion:Theory and applications[C]//10th World Congress on Structural and Multidisciplinary Optimization. Orlando, USA, 2013.
[13] 李典庆, 蒋水华. 边坡可靠度非侵入式随机分析方法[M]. 北京:科学出版社, 2016. LI D Q, JIANG S H. Non-intrusive stochastic analysis method of slope reliability[M]. Beijing:Science Press, 2016. (in Chinese)
[14] 蒋水华, 冯晓波, 李典庆, 等. 边坡可靠度分析的非侵入式随机有限元法[J]. 岩土力学, 2013, 34(8):2347-2354. JIANG S H, FENG X B, LI D Q, et al. Reliability analysis of slope using non-intrusive stochastic finite element method[J]. Rock and Soil Mechanics, 2013, 34(8):2347-2354. (in Chinese)
[15] HALDAR A, MAHADEVAN S. Reliability assessment using stochastic finite element analysis[M]. New York:John Wiley & Sons, 2000.
[16] O'HAGAN A. Polynomial chaos:A tutorial and critique from a statistician's perspective[EB/OL]. (2013-03-24). http://www.tonyohagan.co.uk/academic/pdf/Polynomial-chaos.pdf.
[17] XIU D B. Generalized (Wiener-Askey) polynomial chaos[D]. Providence:Brown University, 2004.
[18] WüNSCHE A. Hermite and Laguerre 2D polynomials[J]. Journal of Computational and Applied Mathematics, 2001, 133(1-2):665-678.
[19] 蒋水华, 张曼, 李典庆. 基于Hermite正交多项式逼近法的重力坝可靠度分析[J]. 武汉大学学报(工学版), 2011, 44(2):170-174. JIANG S H, ZHANG M, LI D Q. Reliability analysis of gravity dam using Hermite orthogonal polynomials approximation method[J]. Engineering Journal of Wuhan University, 2011, 44(2):170-174. (in Chinese)
[20] 吕泰仁, 吴世伟. 用几何法求构件的可靠指标[J]. 河海大学学报(自然科学版), 1988, 16(5):86-93. LYU T R, WU S W. Geometric method for solving reliability index of structures[J]. Journal of Hohai University (Natural Sciences), 1988, 16(5):86-93. (in Chinese)