基于合理子域的改进响应面方法

赵维涛; 邱志平

doi:10.6052/0459-1879-13-339

基于合理子域的改进响应面方法

赵维涛¹,
邱志平²

1.
沈阳航空航天大学航空航天工程学部, 沈阳 110136
2. 北京航空航天大学固体力学研究所, 北京 100191

基金项目: 航空基金（2013ZA54004）和国家自然科学基金（10872017）资助项目.

详细信息

作者简介:
赵维涛，副教授，主要研究方向：结构可靠性.E-mail：zhwt201@163.com

中图分类号: O213.2
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出版历程
- 收稿日期: 2013-10-13
- 修回日期: 2013-12-29
- 刊出日期: 2014-05-17

AN IMPROVED RESPONSE SURFACE METHOD BASED ON THE RESONABLE SUBDOMAIN

Zhao Weitao¹,
Qiu Zhiping²

1.
Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China
2. Institute of Solid Mechanics, Beihang University, Beijing 100191, China

Funds: The project was supported by the Aviation Foundation of China (2013ZA54004) and the National Natural Science Foundation of China (10872017).

摘要

摘要: 基于结构可靠性分析理论，给出了合理子域概念.合理子域能够明确在设计点附近对失效概率起主要贡献区域尺寸，且能够保证失效点以一定概率落在其内，解决了对失效概率起主要贡献区域尺寸难以量化问题.基于合理子域概念，给出了一种改进响应面方法.该方法能够保证响应函数在设计点处是无误差的、且在合理子域内对极限状态函数具有较好近似.采取蒙特卡罗重要抽样方法求解失效概率，结合抽样点位置采取分区域评估方法以提高失效概率求解精度.算例表明，所提方法在处理具有显式和隐式极限状态函数的可靠性分析时，均具有较好的计算精度和较高的计算效率.
- 结构可靠性 /
- 响应面 /
- 合理子域 /
- 失效概率
Abstract: The concept of reasonable subdomain is defined based on the theory of structural reliability in the paper. The size of domain around the design point which gives the main contribution to the failure probability is well-defined by using the reasonable subdomain. The failure points can be distributed in the reasonable subdomain in terms of a given probability. The proposed reasonable subdomain can solve the problem that the size of main domain influencing failure probability is not given obviously. Then, an improved response surface method is also proposed based on the reasonable subdomain. The proposed method can ensure that there is no fitting error of the response function at the design point, and can better fit the limit state function in the reasonable subdomain. The failure probability is evaluated by using the importance sampling Monte Carlo simulation. In order to improve the evaluation accuracy of failure probability, the evaluation method of subdomain is applied according to the locations of sample points. Numerical examples are shown that the proposed method has high accuracy and efficiency for both explicit and implicit limit states.
- structural reliability /
- response surface method /
- reasonable subdomain /
- failure probability

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参考文献(17)

Bucher CG, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Structural Safety, 1990, 7(1): 57-66

Rajashekhar MR, Ellingwood BR. A new look at the response surface approach for reliability analysis. Structural Safety, 1993, 12(3): 205-220

Nguyen XS, Sellier A, Duprat F, et al. Adaptive response surface method based on a double weighted regression technique. Probabilistic Engineering Mechanics, 2009, 24(2): 135-143

Kang SC, Koh HM, Choo JF. An efficient response surface method using moving least squares approximation for structural reliability analysis. Probabilistic Engineering Mechanics, 2010, 25(4): 365-371

Duprat F, Sellier A. Probabilistic approach to corrosion risk due to carbonation via an adaptive response surface method. Probabilistic Engineering Mechanics, 2006, 21(3): 207-216

Allaix DL, Carbone VI. An improvement of the response surface method. Structural Safety, 2011, 33(2): 165-172

Richard B, Cremona C, Adelaide L. A response surface method based on support vector machines trained with an adaptive experimental design. Structural Safety, 2012, 39(1): 14-21

李洪双,吕震宙.结构可靠性分析的支持向量机的响应面法.计算力学学报, 2009, 26(2):199-203 (Li Hongshuang, Lü Zhenzhou. A support vector machine response surface method for structural reliability analysis. Chinese Journal of Computational Mechanics, 2009, 26(2): 199-203 (in Chinese))

吕震宙,赵洁,岳珠峰. 机械结构可靠性分析的高精度响应面法.应用数学和力学,2007, 1(28): 17-24 (Lü Zhenzhou, Zhao Jie, Yue Zhufeng. Advanced response surface method for mechanical reliability analysis. Applied Mathematics and Mechanics, 2007, 1(28): 17-24 (in Chinese))

程晔,周翠英,黄林冲等. 基于缩减样本窗口的响应面重构方法. 计算力学学报, 2011, 28(5): 699-704 (Cheng Ye, Zhou Cuiying, Huang Linchong et al. Sequential response surface reconstructing method based on reducing sampling windows. Chinese Journal of Computational Mechanics, 2011, 28(5): 699-704 (in Chinese))

Weitao Z, Zhiping Q. An efficient response surface method and its application to structural reliability and reliability-based optimization. Finite Elements in Analysis and Design, 2013, 67: 34-42

Weitao Z, Zhiping Q, Yi Y. An efficient response surface method considering the nonlinear trend of the actual limit state. Structural Engineering and Mechanics, 2013, 47(1): 45-58

Guan XL, Melchers RE. Effect of response surface parameter variation on structural reliability estimates. Structural Safety, 2001, 23: 429-444

Gavin HP, Yau CS. High-order limit state functions in the response surface method for structural reliability analysis. Structural Safety, 2008, 30: 162-179

Elegbede C. Structural reliability assessment based on particles swarm optimization. Structural Safety, 2005, 27(2): 171-186

Blatmana G, Sudret B. An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Engineering Mechanics, 2010, 25(2): 183-197

Roussouly N, Petitjean F, Salaun M. A new adaptive response surface method for reliability analysis. Probabilistic Engineering Mechanics, 2013, 32: 103-105