Structural optimization under dynamic reliability constraints by synthesizing change of probability measure and globally convergent method of moving asymptotes

被引：0

作者：

Yang J.-S. ^{[1
,2
]}

Chen J.-B. ^{[1
,2
]}

机构：

[1] State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai

[2] College of Civil Engineering, Tongji University, Shanghai

来源：

Zhendong Gongcheng Xuebao/Journal of Vibration Engineering | 2022年 / 35卷 / 01期

关键词：

Change of probability measure; Dynamic reliability; Probability density evolution method; Reliability optimization design; Stochastic dynamical system;

D O I：

10.16385/j.cnki.issn.1004-4523.2022.01.008

中图分类号：

学科分类号：

摘要：

Dynamic-reliability-based design optimization is a reasonable framework for the optimization of stochastic dynamical systems. In the present paper, a method is proposed for solving dynamic-reliability-based design optimization problems where design variables are considered as the mean values of the probability density functions of part of the random variables involved in the system. In this method, the reliability of stochastic dynamical system is evaluated efficiently by the probability density evolution method (PDEM). Then, by performing the changes of probability measure(COM), the sensitivity of the dynamic reliability with respect to design variables can be efficiently estimated without any additional structural analysis. By incorporating the PDEM-COM synthesized method into a globally convergent version of the method of moving asymptote, dynamic-reliability-based design optimization problems can be solved efficiently. The effectiveness of the proposed method is verified by two numerical examples. The results of the numerical examples indicate that the proposed method is efficient and robust. © 2022, Editorial Board of Journal of Vibration Engineering. All right reserved.

引用

页码：72 / 81

页数：9

共 35 条

[21]

Svanberg K., A class of globally convergent optimization methods based on conservative convex separable approximations, SIAM Journal on Optimization, 12, 2, pp. 555-573, (2002)

[22]

Svanberg K., MMA and GCMMA-two methods for nonlinear optimization, (2007)

[23]

Jensen H A, Sepulveda J G., Structural optimization of uncertain dynamical systems considering mixed-design variables, Probabilistic Engineering Mechanics, 26, 2, pp. 269-280, (2011)

[24]

Li J, Chen J., The principle of preservation of probability and the generalized density evolution equation, Structural Safety, 30, 1, pp. 65-77, (2008)

[25]

Jiang Z M, Li J., Analytical solution of the generalized probability density evolution equation of three classes stochastic systems, Chinese Journal of Theoretical and Applied Mechanics, 48, 2, pp. 413-421, (2016)

[26]

Chen J B, Yang J Y, Li J., A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters, Structural Safety, 59, pp. 20-31, (2016)

[27]

Chen J B, Chan J P., Error estimate of point selection in uncertainty quantification of nonlinear structures involving multiple nonuniformly distributed parameters, International Journal for Numerical Methods in Engineering, 118, 9, pp. 536-560, (2019)

[28]

Yang D X, Liu L B., Reliability analysis of structures with complex limit state functions using probability density evolution method, Structural and Multidisciplinary Optimization, 50, 2, pp. 275-286, (2014)

[29]

Li J, Chen J B., Probability density evolution method for dynamic reliability analysis of stochastic structures, Journal of Vibration Engineering, 17, 2, pp. 5-9, (2004)

[30]

Chen J B, Li J., The extreme value probability density function based method for dynamic reliability assessment of stochastic structures, Earthquake Engineering and Engineering Vibration, 24, 6, pp. 39-44, (2004)

← 1 2 3 4 →