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CLC number: TH122

On-line Access: 2016-11-03

Received: 2016-02-02

Revision Accepted: 2016-05-19

Crosschecked: 2016-10-20

Cited: 1

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Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jin Cheng

http://orcid.org/0000-0002-3254-9976

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Journal of Zhejiang University SCIENCE A 2016 Vol.17 No.11 P.841-854

http://doi.org/10.1631/jzus.A1600143


Direct reliability-based design optimization of uncertain structures with interval parameters


Author(s):  Jin Cheng, Ming-yang Tang, Zhen-yu Liu, Jian-rong Tan

Affiliation(s):  State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   cjinpjun@zju.edu.cn, liuzy@zju.edu.cn

Key Words:  Reliability-based design optimization, Uncertain structure, Degree of interval reliability violation (DIRV), DIRV-based preferential guideline, Direct interval optimization, Nested genetic algorithm (GA)


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Jin Cheng, Ming-yang Tang, Zhen-yu Liu, Jian-rong Tan. Direct reliability-based design optimization of uncertain structures with interval parameters[J]. Journal of Zhejiang University Science A, 2016, 17(11): 841-854.

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Abstract: 
In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.

This paper aims to present an interval reliability-based design optimization method for uncertain structures with bounded parameters, which proposed the concept of DIRV and the DIRV-based preferential guidelines, and integrates the GA and Kriging technique for solving the interval reliability-based optimization model. A typical numerical example, as well as an engineering application is applied to demonstrate the effectiveness of the proposed method. This paper is overall well written in language and focused on a very interesting research topic.

含区间参数的不确定性结构直接可靠性设计优化

目的:为提高含区间参数不确定性结构的可靠性,提供一种基于区间模型的不确定性结构的高效可靠性设计优化方法。
创新点:1. 提出结构性能指标区间可靠度的统一计算公式;2. 提出区间可靠度违反度的概念和基于区间可靠度违反度的优于关系准则;3. 提出并实现区间可靠性优化模型的高效直接智能求解算法。
方法:1. 借鉴图表法并克服其局限,给出计算区间可靠度的统一公式(公式2);2. 利用Kriging近似模型和内层遗传算法计算结构性能指标在不确定性参数影响下的变化区间,从而计算出区间可靠性优化模型中各结构性能指标的区间可靠度及其违反度;3. 基于区间可靠度违反度的优于关系准则,通过外层遗传算法实现各结构设计矢量的直接优劣排序和区间可靠性优化模型的直接智能求解;4. 通过典型算例(图3和4、表2)和工程应用实例(图8和9、表7)验证所提方法的有效性和相比间接求解方法的优越性。
结论:1. 考虑结构性能指标可靠性要求的不确定性结构区间可靠性设计优化模型能够有效反映实际工程中提高不确定结构可靠性的需求;2. 引入区间可靠度违反度的概念和基于可靠度违反度的优于关系准则,利用嵌套遗传算法和Kriging近似模型可实现不确定性结构区间可靠性优化模型的直接高效智能求解;3. 提出的区间可靠性优化模型直接求解方法能比间接方法获得更优的解。

关键词:可靠性设计优化;不确定性结构;区间可靠性违反度;优于关系准则;直接区间优化;嵌套遗传算法

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Reference

[1]Allen, M., Maute, K., 2004. Reliability-based design optimization of aeroelastic structures. Structural and Multidisciplinary Optimization, 27(4):228-242.

[2]Ben-Haim, Y., 1994. A non-probabilistic concept of reliability. Structural Safety, 14(4):227-245.

[3]Ben-Haim, Y., 1995. A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Structural Safety, 17(2):91-109.

[4]Ben-Haim, Y., 2004. Uncertainty, probability and information-gaps. Reliability Engineering & System Safety, 85(1-3):249-266.

[5]Cheng, J., Feng, Y.X., Tan, J.R., et al., 2008. Optimization of injection mold based on fuzzy moldability evaluation. Journal of Materials Processing Technology, 208(1-3):222-228.

[6]Cheng, J., Duan, G.F., Liu, Z.Y., et al., 2014. Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 15(10):774-788.

[7]Cheng, J., Liu, Z.Y., Wu, Z.Y., et al., 2015. Robust optimization of structural dynamic characteristics based on adaptive Kriging model and CNSGA. Structural and Multidisciplinary Optimization, 51(2):423-437.

[8]Cheng, J., Liu, Z.Y., Wu, Z.Y., et al., 2016. Direct optimization of uncertain structures based on degree of interval constraint violation. Computers & Structures, 164:83-94.

[9]Cheng, X.F., Zhang, X., 2011. The robust reliability optimization of steering mechanism for trucks based on non-probabilistic interval model. Key Engineering Materials, 467-469:296-299.

[10]Costa, C.B.B., Maciel, M.R.W., Maciel Filho, R., 2005. Factorial design technique applied to genetic algorithm parameters in a batch cooling crystallization optimization. Computers & Chemical Engineering, 29(10):2229-2241.

[11]Deb, K., Gupta, S., Daum, D., et al., 2009. Reliability based optimization using evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 13(5):1054-1074.

[12]Du, X.P., 2012. Reliability-based design optimization with dependent interval variables. International Journal for Numerical Methods in Engineering, 91(2):218-228.

[13]Elishakoff, I., 1995a. Discussion on a non-probabilistic concept of reliability. Structural Safety, 17(3):195-199.

[14]Elishakoff, I., 1995b. Essay on uncertainties in elastic and viscoelastic structures: from AM Freudenthal’s criticisms to modern convex modeling. Computers & Structures, 56(6):871-895.

[15]Elishakoff, I., Ohaski, M., 2010. Optimization and Anti-optimization of Structures under Uncertainty. Imperial College Press, London, UK.

[16]Elishakoff, I., Elettro, F., 2014. Interval, ellipsoidal, and super-ellipsoidal calculi for experimental and theoretical treatment of uncertainty: which one ought to be preferred International Journal of Solids and Structures, 51(7-8):1576-1586.

[17]Elishakoff, I., Haftka, R.T., Fang, J., 1994. Structural design under bounded uncertainty-optimization with anti-optimization. Computers & Structures, 53(6):1401-1405.

[18]Elishakoff, I., Wang, X.J., Hu, J.X., et al., 2013. Minimization of the least favorable static response of a two-span beam subjected to uncertain loading. Thin-Walled Structures, 70:49-56.

[19]Fernandez-Prieto, J.A., Canada-Bago, J., Gadeo-Martos, M.A., et al., 2011. Optimisation of control parameters for genetic algorithms to test computer networks under realistic traffic loads. Applied Soft Computing, 11(4):3744-3752.

[20]Ge, R., Chen, J.Q., Wei, J.H., 2008. Reliability-based design of composites under the mixed uncertainties and the optimization algorithm. Acta Mechanica Solida Sinica, 21(1):19-27.

[21]Guo, S.X., Lv, Z.Z., Feng, Y.S., 2001. A non-probabilistic model of structural reliability based on interval analysis. Chinese Journal of Computational Mechanics, 18(1):56-60 (in Chinese).

[22]Guo, S.X., Zhang, L., Li, Y., 2005. Procedures for computing the non-probabilistic reliability index of uncertain structures. Chinese Journal of Computational Mechanics, 22(2):227-231 (in Chinese).

[23]Inuiguchi, M., Sakawa, M., 1995. Minimax regret solution to linear programming problems with an interval objective function. European Journal of Operational Research, 86(3):526-536.

[24]Inuiguchi, M., Sakawa, M., 1997. An achievement rate approach to linear programming problems with an interval objective function. Journal of the Operational Research Society, 48(1):25-33.

[25]Jiang, C., 2008. Uncertainty Optimization Theory and Algorithm Based on Interval. PhD Thesis, Hunan University, Changsha, China (in Chinese).

[26]Jiang, C., Han, X., Guan, F.J., et al., 2007. An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method. Engineering Structures, 29(11):3168-3177.

[27]Jiang, C., Han, X., Liu, G.P., 2008a. A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188(1):1-13.

[28]Jiang, C., Han, X., Liu, G.P., 2008b. A sequential nonlinear interval number programming method for uncertain structures. Computer Methods in Applied Mechanics and Engineering, 197(49-50):4250-4265.

[29]Jiang, C., Han, X., Liu, G.P., 2008c. Uncertain optimization of composite laminated plates using a nonlinear number programming method. Computers & Structures, 86(17-18):1696-1703.

[30]Jiang, C., Li, W.X., Han, X., et al., 2011. Structural reliability analysis based on random distributions with interval parameters. Computers & Structures, 89(23-24):2292-2302.

[31]Jiang, C., Zhang, Z., Han, X., et al., 2013. A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty. Computers & Structures, 129:1-12.

[32]Jiang, T., Chen, J.J., Xu, Y.L., 2007. A semi-analytic method for calculating non-probabilistic reliability index based on interval models. Applied Mathematical Modelling, 31(7):1362-1370.

[33]Kucukkoc, I., Karaoglan, A.D., Yaman, R., 2013. Using response surface design to determine the optimal parameters of genetic algorithm and a case study. International Journal of Production Research, 51(17):5039-5054.

[34]Kundu, A., Adhikari, S., Friswell, M.I., 2014. Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty. International Journal for Numerical Methods in Engineering, 100(3):183-221.

[35]Luo, Z., Chen, L.P., Yang, J.Z., et al., 2006. Fuzzy tolerance multilevel approach for structural topology optimization. Computers & Structures, 84(3-4):127-140.

[36]Missoum, S., Ramu, P., Haftka, R.T., 2007. A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems. Computer Methods in Applied Mechanics and Engineering, 196(29-30):2895-2906.

[37]Qi, W.C., Qiu, Z.P., 2013. Non-probabilistic reliability-based structural design optimization based on interval analysis methods. Scientia Sinica Physica, Mechanica & Astronomica, 43(1):85-93 (in Chinese).

[38]Qiu, Z.P., Chen, S.H., Elishakoff, I., 1995. Natural frequencies of structures with uncertain but nonrandom parameters. Journal of Optimization Theory and Applications, 86(3):669-683.

[39]Qiu, Z.P., Mueller, P.C., Frommer, A., 2004. The new nonprobabilistic criterion of failure for dynamical systems based on convex models. Mathematical and Computer Modelling, 40(1-2):201-215.

[40]Verhaeghe, W., Elishakoff, I., Desmet, W., et al., 2013. Uncertain initial imperfections via probabilistic and convex modeling: axial impact buckling of a clamped beam. Computers & Structures, 121:1-9.

[41]Wang, X.J., Qiu, Z.P., 2009. Non-probabilistic interval reliability analysis of wing flutter. AIAA Journal, 47(3):743-748.

[42]Wang, X.J., Qiu, Z.P., Elishakoff, I., 2008. Non-probabilistic set-theoretic model for structural safety measure. Acta Mechanica, 198(1-2):51-64.

[43]Wu, J.L., Luo, Z., Zhang, Y.Q., et al., 2013. Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions. International Journal for Numerical Methods in Engineering, 95(7):608-630.

[44]Wu, J.L., Luo, Z., Zhang, Y.Q., et al., 2014. An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels. Applied Mathematical Modelling, 38(15-16):3706-3723.

[45]Wu, J.L., Luo, Z., Zhang, N., et al., 2015a. A new interval uncertain optimization method for structures using Chebyshev surrogate models. Computers & Structures, 146: 185-196.

[46]Wu, J.L., Luo, Z., Zhang, N., et al., 2015b. A new uncertain analysis method and its application in vehicle dynamics. Mechanical Systems and Signal Processing, 50-51:659-675.

[47]Xia, B.Z., Lu, H., Yu, D.J., et al., 2015. Reliability-based design optimization of structural systems under hybrid probabilistic and interval model. Computers & Structures, 160:126-134.

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