On the consistency issue of adjoint methods for sensitivity analysis of dynamic response

PDF(1444 KB)

Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (20) : 167-173.

HU Zhi-qiang1，MA Hai-tao1,2

Author information +

History +

Abstract

The inconsistency issue of adjoint variable methods (AVMs) for sensitivity analysis of transient dynamic responses is investigated. The differentiate-then-discretize and discretize-then-differentiate approaches are considered, focusing on their computational accuracy, convergence rates and result consistency. Based on the basic idea of the ex-plicit time-domain method for dynamic analysis, a concise discretize-then-differentiate AVM formulation is presented. It is found that the inconsistency of the differentiate-then-discretize approach is caused by the fact that numerical solutions for dynamic responses satisfy equations of motion only at integration points in the time domain, and despite this consis-tency problem, this approach is still reliable for sensitivity analysis of dynamic responses.

Key words

sensitivity analysis / adjoint variable method / consistency / transient dynamic response

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

HU Zhi-qiang1，MA Hai-tao1,2. On the consistency issue of adjoint methods for sensitivity analysis of dynamic response[J]. Journal of Vibration and Shock, 2015, 34(20): 167-173

References

[1] 陈太聪,韩大建,苏成. 参数灵敏度分析的神经网络方法及其工程应用[J]. 计算力学学报, 2004, 21(6): 752-756.
CHEN Tai-cong, HAN Da-jian, SU Cheng. Neural network method in parameter sensitivity analysis and its application in engineering [J]. Chinese Journal of Computational Mechanics, 2004, 21(6): 752-756.
[2] 陈钢,赵国忠,顾元宪. 声场-结构耦合系统灵敏度分析及优化设计研究[J]. 振动与冲击, 2007, 26(4): 86-89.
CHEN Gang, ZHAO Guo-zhong, GU Yuan-xian. Sensitivity analysis and design optimization method for acoustic- structural coupled systems[J]. Journal of Vibration and Shock, 2007, 26(4): 86-89.
[3] 毛玉明,郭杏林,赵岩,等. 基于灵敏度分析的结构动态载荷识别研究[J]. 振动与冲击, 2010, 29(10): 1-3.
MAO Yu-ming, GUO Xing-lin, ZHAO Yan, et al. Force iden-tification based on sensitivity analysis method [J]. Journal of Vibration and Shock, 2010, 29(10): 1-3.
[4] 赵杰,李峰,刘录. 基于有限元的超高压管线系统振动特性灵敏度分析 [J]. 振动与冲击, 2014, 33(10): 148-151.
ZHAO Jie, LI Feng, LIU Lu. Vibration characteristic sensitiv-ity analysis based on finite element for ultra-high pressure pipeline systems[J].Journal of Vibration and Shock, 2014, 33(10): 148-151.
[5] Dahl J, Jensen J S, Sigmund O. Topology optimization for transient wave propagation problems in one dimension[J]. Structural and Multidisciplinary Optimization,2008,36:585- 595.
[6] Kang Z, Zhang X P, Jiang S G,et al. On topology optimization of damping layer in shell structures under harmonic excitations[J]. Structural and Multidisciplinary Optimization, 2012, 46: 51-67.
[7] Le C, Bruns T E, Tortorelli D A. Material microstructure optimization for linear elastodynamic energy wave management[J]. Journal of the Mechanics and Physics of Solids,2012, 60: 351-378.
[8] Kang B S, Park G J, Arora J S. A review of optimization of structures subjected to transient loads[J]. Structural and Multi¬disciplinary Optimization,2006, 31: 81-95.
[9] Keulen F V, Haftka R T, Kim N H. Review of options for structural design sensitivity analysis,part 1: linear systems [J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194: 3213-3243.
[10] Jensen J S, Nakshatrala P B,Tortorelli D A. On the consis-tency of adjoint sensitivity analysis for structural optimization of linear dynamic problems[J]. Structural and Multidiscipli-nary Optimization, 2014, 49(5): 831-837.
[11] Bathe K J. Finite element procedures[M]. Prentice-Hall, Englewood Cliffs, New Jersey, 1996.
[12] Kreyszig E. Advanced engineering mathematics (7th edn) [M]. New York:Wiley, 1993.
[13] 苏成,徐瑞.非平稳激励下结构随机振动时域分析法[J]. 工程力学, 2010, 27(12): 77-83.
SU Cheng, XU Rui. Random vibration analysis of structures subjected to non-stationary excitations by time domain method [J]. Engineering Mechanics, 2010, 27(12): 77-83.
[14] Cook R D, Malkus D S, Plesha M E, et al. Concepts and ap-plications of finite element analysis(4th edn)[M]. New York: Wiley,2000.