In the reliability analysis and design of structures, it is unreasonable to describe all the uncertain parameters as stochastic variables when the probabilistic distribution characteristic for some of them is unavailable and only their variation bounds are known. Based on the probabilistic model description and the multi-ellipsoid model description for different types of uncertainties, a reliability-based optimization model of structures combining stochastic and bounded uncertainties is mathematically formulated with constraints on mixed reliability indices defined in standard U-space. The performance measure approach is employed to transform the original model into its equivalent form for improving the convergence and the stability. Then the reformulated nested optimization problem is simplified into a series of deterministic ones by using the sequential approximate programming approach, which greatly facilitates the efficient solution. Two examples, a mathematic optimization problem and a design of missile wing structure, are given to illustrate the validity of the proposed model as well as the efficiency of the presented numerical techniques.
LUO Yangjun, GAO Zongzhan, YUE Zhufeng, WU Ziyan
. Reliability-based Optimization Design for Structures with Stochastic and Bounded Parameter Uncertainties[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011
, 32(6)
: 1058
-1066
.
DOI: CNKI:11-1929/V.20110310.1709.001
[1] Valdebenito M A, Schuller G I. A survey on approaches for reliability-based optimization[J]. Structural and Multi-disciplinary Optimization, 2010, 42(5): 645-663.
[2] Melchers R E. Structural reliability analysis and prediction[M]. 2nd ed. Chichester: Wiley, 1999.
[3] Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A.M. Freudenthal’s criticisms to modern convex modeling[J]. Computers and Structures, 1995, 56(6): 871-895.
[4] Sexsmith R G. Probability-based safety analysis—value and drawbacks[J]. Structural Safety, 1999, 21(4): 303-310.
[5] Moens D, Vandepitte D. Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis[J]. Archives of Computational Methods in Engineering, 2006, 13(3): 389-464.
[6] Mller B, Beer M. Engineering computation under uncertainty—capabilities of non-traditional models[J]. Computers and Structures, 2008, 86(10): 1024-1041.
[7] Ben-Haim Y, Elishakoff I. Convex models of uncertainty in applied mechanics[M]. Amsterdam: Elsevier, 1990.
[8] Jiang C, Han X, Liu G R. Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(49-52): 4791-4800.
[9] 亢战, 罗阳军. 基于凸模型的结构非概率可靠性优化[J]. 力学学报, 2006, 38(6): 807-815. Kang Zhan, Luo Yangjun. On structural optimization for non-probabilistic reliability based on convex models[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 807-815. (in Chinese)
[10] Elishakoff I, Colombi P. Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters[J]. Computer Methods in Applied Mechanics and Engineering, 1993, 104(2): 187-209.
[11] Oberkampf W L, Helton J C, Joslyn C A, et al. Challenge problems: uncertainty in system response given uncertain parameters[J]. Reliability Engineering and System Safety, 2004, 85(1-3): 11-19.
[12] Penmetsa R C, Grandhi R V. Efficient estimation of structural reliability for problems with uncertain intervals[J]. Computers and Structures, 2002, 80(12): 1103-1112.
[13] Karanki D R, Kushwaha H S, Verma A K, et al. Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment[J]. Risk Analysis, 2009, 29(5): 662-675.
[14] Qiu Z, Wang J. The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system[J]. Engineering Failure Analysis, 2010, 17(5): 1142-1154.
[15] Gao W, Song C, Tin-Loi F. Probabilistic interval analysis for structures with uncertainty[J]. Structural Safety, 2010, 32(3): 191-199.
[16] 郭书祥, 吕震宙. 结构可靠性分析的概率和非概率混合模型[J]. 机械强度, 2002, 24(4): 524-526. Guo Shuxiang, Lu Zhenzhou. Hybrid probabilistic and non-probabilistic model of structural reliability[J]. Journal of Mechanical Strength, 2002, 24(4): 524-526. (in Chinese)
[17] Du X, Sudjianto A, President S V, et al. Reliability-based design with the mixture of random and interval variables[J]. Journal of Mechanical Design, 2005, 127(6): 1068-1076.
[18] 程远胜, 钟玉湘, 游建军. 概率及非概率不确定性条件下结构鲁棒设计方法[J]. 工程力学, 2005, 22(4): 10-14. Cheng Yuansheng, Zhong Yuxiang, You Jianjun. Structural robust design subject to probabilistic and non-probabilistic uncertainties[J]. Engineering Mechanics, 2005, 22(4): 10-14. (in Chinese)
[19] Tu J, Choi K K, Park Y H. A new study on reliability-based design optimization[J]. Journal of Mechanical Design, 1999, 121(4): 557-564.
[20] Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J]. Computers and Structures, 1978, 9(5): 489-494.
[21] Rosenblatt M. Remarks on a multivariate transformation[J]. Annals of Mathematical Statistics, 1952, 23(3): 470-472.
[22] Luo Y, Kang Z, Li A. Structural reliability assessment based on probability and convex set mixed model[J]. Computers and Structures, 2009, 87(21-22): 1408-1415.
[23] Lee J O, Yang Y S, Ruy W S. A comparative study on reliability-index and target-performance-based probabilistic structural design optimization[J]. Computers and Structures, 2002, 80(3): 257-269.
[24] Liang J, Mourelatos Z P, Tu J. A single-loop method for reliability-based design optimization[J]. International Journal of Product Development, 2008, 5(1): 76-92.
[25] Cheng G, Xu L, Jiang L. A sequential approximate programming strategy for reliability-based structural optimization[J]. Computers and Structures, 2006, 84(21): 1353-1367.
[26] Du X, Chen W. Sequential optimization and reliability assessment method for efficient probabilistic design[J]. Journal of Mechanical Design, 2004, 126(2): 225-233.
[27] Neumaier A, Pownuk A. Linear systems with large uncertainties, with applications to truss structures[J]. Reliable Computing, 2007, 13(2): 149-172.
[28] Lawrence C, Zhou J L, Tits A L. User’s guide for CFSQP version 2.5. . http://www.aemdesign.com.
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