有界不确定结构基于最小二乘支持向量机回归的动力特性分析方法

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (7) : 199-207.

论文

莫延彧1, 郭书祥2, 唐承2

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Dynamic characteristics analysis method for uncertain-but-bounded structures based on least squares SVM regression

MO Yanyu1,GUO Shuxiang2,TANG Cheng2

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摘要

针对不确定结构的动力特性分析问题展开研究，考虑仅已知结构参数变量变化范围的情况，建立不确定参数变量的区间模型。对不确定变量在其取值范围内进行改进的均匀试验设计抽样，并基于确定结构动力特性分析的有限元法和模态叠加理论，提出改进均匀试验设计抽样模拟方法；考虑到该算法计算效率较低，对其进行改进并提出基于最小二乘支持向量机回归的模拟方法，算法在不改变样本点数量的前提下，引入了支持向量机回归代理模型，用训练后的代理模型对不确定结构的动力特性进行了模拟分析。算法通过两个数值算例验证了其有效性。

Abstract

Dynamic properties analysis for uncertain-but-bounded structures was studied.To reach this goal,uncertain-but-bounded parameters were taken as interval variables,but the distributions of the variables were unknown,and then an interval model was built for each uncertain variable.After an improved uniform design sampling for each interval variable,a dynamic analysis simulation method for uncertain structures was proposed based on the deterministic structure’s dynamic properties analysis with the finite element method and the modal superposition theory.Considering the poor efficiency of the proposed method,an improved method was presented.The improved method was based on the least squares support vector machine (SVM) regression in the premise of unchanged number of sampling points,a surrogate model of SVM regression was introduced.The dynamic characteristics of uncertain structures were simulated and analyzed with this surrogate model trained.Finally,two different numerical examples demonstrated the validity of the proposed approach.

Key words

uniform design / interval model / frequency analysis / frequency response analysis / support vector machine (SVM) regression

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莫延彧1, 郭书祥2, 唐承2. 有界不确定结构基于最小二乘支持向量机回归的动力特性分析方法[J]. 振动与冲击, 2017, 36(7): 199-207

MO Yanyu1,GUO Shuxiang2,TANG Cheng2. Dynamic characteristics analysis method for uncertain-but-bounded structures based on least squares SVM regression[J]. Journal of Vibration and Shock, 2017, 36(7): 199-207

参考文献

[1] Ben-haim Y, Elishakoff I. Convex models of uncertainty in applied mechanics[M]. Elsevier Science Publisher, Amsterdam, 1990.
[2] 王登刚. 计算具有区间参数结构的固有频率的优化方法[J]. 力学学报，2004,36(3): 364-372.
Wang Denggang. Global optimization method for computing frequencies of structures with interval uncertain parameters[J]. ACTA MECHANICA SINICA, 2004,36(3): 364-372.
[3] 张建国, 陈建军, 马孝松, 胡太彬. 不确定结构动力特征值区间分析的一种算法[J]. 应用力学学报，2006,23(1): 96-100.
Zhang Jianguo, Chen Jianjun, Ma Xiaosong, etc. Method for dynamic eigenvalues interval analysis of uncertain structures[J]. Chinese Journal of Applied Mechanics, 2006,23(1): 96-100.
[4] 马梁 ,陈塑寰 ,孟广伟. 区间参数有大变化时的结构特征值分析[J]. 吉林大学学报（工学版），2009,39(1): 98-102.
Ma Liang, Chen Su-huan, Meng Guang-wei. Eigenvalue analysis of structures with large variations of interval parameters[J]. Journal of Jilin University(Engineering and Technology Edition), 2009,39(1):98-102.
[5] G. Manson. Calculating frequency response functions for uncertain systems using complex affine analysis[J]. Journal of Sound and Vibration, 2005,288(3):487–521.
[6] Hilde De Gersem, David Moens, Wim Desmet, Dirk Vandepitte. Interval and fuzzy dynamic analysis of finite element models with superelements[J]. Computers & Structures, 2007, 85(5-6):304-319.
[7] Maarten De Munck, David Moens, Wim Desmet, Dirk Vandepitte. A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties[J]. Computers & Structures. 2008, 86(10): 1080–1092.
[8] Yang Yaowen, Cai Zhenhan, Liu Yu. Interval analysis of dynamic response of structures using Laplace transform[J]. Probabilistic Engineering Mechanics, 2012,29:32-39.
[9] Ma Yanhong, Liang Zhichao, Chen Meng, Hong Jie. Interval analysis of rotor dynamic response with uncertain parameters[J]. Journal of Sound and Vibration, 2013, 332(16):3869-3880.
[10] A. Sofi, G. Muscolino, I. Elishakoff. Natural frequencies of structures with interval parameters[J]. Journal of Sound and Vibration, 2015,347:79-95.
[11] Fang K-T. The Uniform Design: Application of Number-Theoretic Methods in Experimental Design[J]. Acta Mathematicae Applicatae Sinica, 1980, 3(4):363–372.
[12] Fang K-T, Lin DKJ, Winker P, Zhang Y. Uniform design: Theory and Application[J]. Technometrics, 2000,42(3): 237–248.
[13] K.T. Fang, Y. Wang. Number-theoretic Methods in Statistics[M]. Chapman and Hall, London, 1994.
[14] Mercer, J. Functions of positive and negative type and their connection with the theory of integral equations[J]. Philosophical Transactions of the Royal Society, 1909, Ser A 209: 415–446.
[15] Xavier de Souza, S, Suykens, J. A. K, Vandewalle, J, & Bollé, D. Coupled Simulated Annealing[J]. IEEE Transactions on Systems, Man and Cybernetics - Part B, 2010,40(2): 320–35.
[16] An S J, Liu W Q, Venkatesh S. Fast cross-validation algorithms for least squares support vector machine and kernel ridge regression[J]. Pattern Recognition, 2007, 40(8):2154－2162.
[17] Yanyu Mo, Shuxiang Guo, and Cheng Tang. A Vibration Reliability Analysis Method for the Uncertain Space Beam Structure[J]. Shock and Vibration, 2016, 2016:14pages.