基于频域非线性方法的铝蜂窝夹层结构动力学特性研究
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摘要
本文在研究大量相关文献的基础上,对非线性系统的辨识方法进行了综述,其中着重描述了频域非线性系统辨识方法,这些频率结果比相应的时域结果有更重要的意义,且它们易于计算和解释。现今铝蜂窝夹层结构广泛应用于工程领域,但由于铝蜂窝夹层结构复杂,使得应用传统的辨识方法难以对其动力学特性给出清楚和完整的描述,本文的目的就是应用随机数据的频域非线性分析与辨识方法对铝蜂窝夹层结构的动力学特性进行辨识。
首先,系统总结了使用一般三阶非线性模型辨识的方法和步骤。得到的结果是用基本的和高阶的谱密度函数以及基本的和高阶的频率响应函数表示的频率函数。
其次,深入阐述了前线性系统与后线性系统的特点与计算方法。对于这些系统它们的高阶频率响应函数将成为单一的频率变量函数。
最后,将随机数据的频域非线性分析与辨识方法应用于某铝蜂窝夹层结构多功能电子机箱的非线性特性研究中。利用前线性系统与后线性系统中的6个模型来分别拟合该系统,从中选取辨识相对误差最小的模型来描述该非线性系统。这种方法能够更准确的分析非线性系统特性,得到该系统的非线性阶数及各阶非线性的频率响应函数,实现了对被试机箱的非线性系统辨识。在此基础之上,从结构材料与结构形式的角度进一步讨论了非线性产生的原因。
利用本文的方法,实现了对铝蜂窝夹层结构动力学特性的辨识,这对铝蜂窝夹层结构的设计,实验和分析具有一定的实用价值。
The identification approaches of nonlinear systems, especially the approaches in frequency domain, are discussed based on investigation of related articles. The frequency results are far more significant and easy to calculate and explain than the ones in time domain. The honeycomb sandwich structure has been widely utilized in engineering field nowadays. However, due to the complex construction of this structure, it seems not quite easy to describe its dynamic characteristic clearly and completely via conventional methods. The purpose of this thesis is to analyze and identify the dynamic characteristic of honeycomb sandwich structure based on nonlinear methods to stochastic data in frequency domain.
First, the methods and procedures of general three orders nonlinear identification are summarized and the results are frequency functions described by basic and high order spectral density functions and frequency response functions.
Secondly, the characteristics and procedures of before linear systems and after linear systems are discussed. It is found that the high order frequency response functions of these systems will become single frequency variable functions.
Finally, the nonlinear identification method to stochastic data in frequency domain is used to analyze and identify the nonlinear characteristic of some multifunctional electrical case with honeycomb sandwich structure. This system is fitted separately by six models of before linear system and after linear system and then the optimal model with minimum relative error is chosen to describe the system. This method can not only analyze the system characteristic accurately, but also get the order and nonlinear frequency response function in every order, therefore realizes the nonlinear system identification of the case under study. The causes of nonlinear are also discussed later based on these results from the view of structure material and form.
To identify the dynamic characteristic of honeycomb sandwich structure via method mentioned in this thesis can be valuable in practice for further design,
首先,系统总结了使用一般三阶非线性模型辨识的方法和步骤。得到的结果是用基本的和高阶的谱密度函数以及基本的和高阶的频率响应函数表示的频率函数。
其次,深入阐述了前线性系统与后线性系统的特点与计算方法。对于这些系统它们的高阶频率响应函数将成为单一的频率变量函数。
最后,将随机数据的频域非线性分析与辨识方法应用于某铝蜂窝夹层结构多功能电子机箱的非线性特性研究中。利用前线性系统与后线性系统中的6个模型来分别拟合该系统,从中选取辨识相对误差最小的模型来描述该非线性系统。这种方法能够更准确的分析非线性系统特性,得到该系统的非线性阶数及各阶非线性的频率响应函数,实现了对被试机箱的非线性系统辨识。在此基础之上,从结构材料与结构形式的角度进一步讨论了非线性产生的原因。
利用本文的方法,实现了对铝蜂窝夹层结构动力学特性的辨识,这对铝蜂窝夹层结构的设计,实验和分析具有一定的实用价值。
The identification approaches of nonlinear systems, especially the approaches in frequency domain, are discussed based on investigation of related articles. The frequency results are far more significant and easy to calculate and explain than the ones in time domain. The honeycomb sandwich structure has been widely utilized in engineering field nowadays. However, due to the complex construction of this structure, it seems not quite easy to describe its dynamic characteristic clearly and completely via conventional methods. The purpose of this thesis is to analyze and identify the dynamic characteristic of honeycomb sandwich structure based on nonlinear methods to stochastic data in frequency domain.
First, the methods and procedures of general three orders nonlinear identification are summarized and the results are frequency functions described by basic and high order spectral density functions and frequency response functions.
Secondly, the characteristics and procedures of before linear systems and after linear systems are discussed. It is found that the high order frequency response functions of these systems will become single frequency variable functions.
Finally, the nonlinear identification method to stochastic data in frequency domain is used to analyze and identify the nonlinear characteristic of some multifunctional electrical case with honeycomb sandwich structure. This system is fitted separately by six models of before linear system and after linear system and then the optimal model with minimum relative error is chosen to describe the system. This method can not only analyze the system characteristic accurately, but also get the order and nonlinear frequency response function in every order, therefore realizes the nonlinear system identification of the case under study. The causes of nonlinear are also discussed later based on these results from the view of structure material and form.
To identify the dynamic characteristic of honeycomb sandwich structure via method mentioned in this thesis can be valuable in practice for further design,
引文
1 李秀英, 韩志刚. 非线性系统辨识方法的新进展. 自动化技术与应用. 2004, 23(10):5~7
2 陈昌亚, 王本利, 王德禹, 张建刚. 随振动量级增加卫星结构频率下移的分析. 上海航天. 2004, 16(6):44~47
3 Saito. Takashi, Okuno, Sumio, Kawano, Syunichi. Parameter identification and damping property of aluminum honeycomb sandwich panels. Japan Society of Mechanical Engineering. 1995, 61 (5):871~878
4 T. Saito, R. D. Parbery, S. Okuno, S. Kawano. Parameter identification for aluminum honeycomb sandwich panels based on orthotropic timoshenko beam theory. Journal of Sound and Vibration. 1997, 208(2):271~287
5 Hyeung-Yun Kim, Woonbong Hwang. Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams. Composite Structures. 2002, 55 (1):51~62
6 L H Yam, Y J Yan, L Cheng, J S Jiang. Identification of complex crack damage for honeycomb sandwich plate using wavelet analysis and neural networks. Smart Materials and Structures. 2003, 12(5):661~671
7 陈昌亚, 宋汉文, 王德禹, 陶明德. 卫星结构铝蜂窝板非线性振动试验与参数辨识研究.振动与冲击. 2004,23(1):8~11
8 陈昌亚, 宋汉文, 王德禹, 陶明德. 卫星振动试验中固有频率“漂移"现象初步研究.振动与冲击. 2003,22(4):23~25
9 吴广玉. 系统辨识与自适应. 哈尔滨工业大学出版,1987:56~78
10 张成乾, 张国强. 系统辨识与参数估计. 机械工业出版社,1986:32~69
11 张洪锇, 胡干耀. 现代控制理论(第四册)系统辨识. 北京航空学院出版社,1987:41~80
12 方崇智, 萧德云. 过程辨识. 清华大学出版社, 1988:110~142
13 Merrill W. Identification of multivariable high performance turbofan engine dynamic from closed-loop data. J. Guidance. 1984,7(6):637~652
14 Peter Van O., Bart De M.. Subspace algorithms for the identification of combined deterministic-stochastic system. Automatics. 1994,30(1):75~93
15 马艳 , 曾庆福 , 李志舜 . 子空间辨识方法的改进 . 推进技术 . 2001,22(4):319~321
16 卜雄洙, 范茂军. 测试系统动态参数的时域辨识. 南京理工大学学报. 1995, 19(6):521~524
17 戎海武. 窄带随机噪声作用下强非线性系统的响应. 振动工程学报. 2003, 16(1):81~84
18 戎海武. 窄带随机噪声激励下多自由度非线性系统的响应. 力学季刊. 2003,24(2):211~218
19 赵玉成等. 时间序列关联维数在非线性系统运动性态识别中的应用. 航空学报. 2003,24(1):27~31
20 Motoda, Toshikazu, Miyazawa, Yoshikazu. Identification of influential uncertainties in Monte Carlo analysis. American Inst. Aeronautics and Astronautics Inc. 2002, 39(4):615~623
21 Nordlund P J , Fredrid G.. Sequential Monte Carlo filtering techniques applied to integrated navigation systems. IEEE Proceedings of the American Control Conference. 2001, (6):25~27
22 胡 荣 强 . 实 用 频 域 辨 识 方 法 的 讨 论 与 改 进 . 武 汉 工 学 院 学 报 . 1989,11(4):10~20
23 高 阳, 王三民, 刘晓宁. 一种改进的增量谐波平衡法及其在非线性振动中的应用. 机械科学与术. 2005,24(6):663~665
24 M. Thothandri, R. A. Casas, F. C. Moon, R. Dandrea, C. R. Johnson J.R.. Nonlinear System Identification of Multi-Degree-of-Freedom Systems. Nonlinear Dynamics. 2003, 32(3): 307~322
25 Miichael. A., Shcherbakov. Fast estimation of Wiener kernels of nonlinear systems in the frequency domain. IEEE Signal Processing Workshop on Higher-Order Statistics. 1997:117~121
26 张广莹, 邓正隆. 基于小波分析的非线性系统 Wiener 模型辨识.电机与控制学报. 2001,5(2):95~99
27 George-Othon A., Glentis, Panos Koukoulas, Nicholas Kalouptsidis. Efficient Algorithms for Volterra System Identification. IEEE Transactions on single processing. 1999, 47(11):3042~3057
28 Dorel Aiordachioaie. Detection and classification of non-linearities based on Volterra kernels processing. Engineering Applications of Artificial Intelligence. 2001, 14 (6):497~503
29 Animesh Chatterjeea, and Nalinaksh S, Vyas. Non-linear parameter estimation in multi-degree-of-freedom systems using multi-input Volterra series. Mechanical Systems and Signal Processing. 2004,18 (4):457~489
30 刘翀等. 基于非线性传递函数理论的非线性内模控制. 自动化技术与应用. 2000,19(5):1~4
31 欧文等. Volterra 泛函级数在非线性系统辨识中的应用. 控制与决策. 2002, 2(17): 239~242
32 Bendat, J. S.. Modern analysis procedures for multiple input/output problems. Journal of Sound and Vibration. 1980, 68(2): 498~512
33 Julius S. Bendat. 随机数据的非线性系统分析与辨识. 沈民奋等译. 西南交通大学出版社,1992:153~200
34 Julius S. Bendat. Robert N. Coppolino, Paul A. Palo. Identification of Physical Parameters with Memory in Non-Linear Systems. Int. J. Non-linear Mechanics. 1995,6(30):841~860
35 刘昆. 铝蜂窝夹层结构卫星频域非线性特性研究. 哈尔滨工业大学硕士论文.2004:9~32
36 王丽丽, 张景绘. 非线性动力学系统的辨识时频滤波与骨架曲线. 应用数学和力学. 2001,2(22):182~190
37 马宝萍, 徐志皋. 基于改进的 Elman 网络的内模控制及其应用. 热能动力工程. 2000, 15(4):429~431
38 魏民祥, 闫桂荣, 沈亚鹏. 基于动态神经网络非线性结构辨识的研究.应用力学学报. 2002,17(2):110~114
39 Billings, S. A. and etc. Properties of Neural Networks with Applications to Modeling Nonlinear Dynamical Systems. Int. J. Contro1. 1992,55(1):193~224
40 X. M. Ren, A. B. Rad, P. T. Chan, Wai Lun Lo. Identification and Control of Continuous-Time Nonlinear Systems via Dynamic Neural Networks. IEEE transactions on industrial electronics. 2003, 50(3):478~456
41 王文韬, 李成军, 田军. 基于一种改进BP神经网络的一类非线性系统辨识方法. 青岛科技大学学报. 2005,26(1):85~88
42 Thapa, B. K., Jones, B., Zhu, Q. M.. Non-linear control with neural networks. International Conference on Knowledge-Based Intelligent Electronic Systems, Proceedings. 2000: 868~873
43 Zhai Donghai, Li Li, Jin Fan. Nonlinear-Systems Model Identification withAdditive Multiplicative Fuzzy Neural Network. 电子科技大学学报. 2004, 33(5):577~581
44 Kosmatopoulos, E. B.. High-order neural network structures for identification of dynamical systems. Neural Networks. 1995, 6(2):422~431
2 陈昌亚, 王本利, 王德禹, 张建刚. 随振动量级增加卫星结构频率下移的分析. 上海航天. 2004, 16(6):44~47
3 Saito. Takashi, Okuno, Sumio, Kawano, Syunichi. Parameter identification and damping property of aluminum honeycomb sandwich panels. Japan Society of Mechanical Engineering. 1995, 61 (5):871~878
4 T. Saito, R. D. Parbery, S. Okuno, S. Kawano. Parameter identification for aluminum honeycomb sandwich panels based on orthotropic timoshenko beam theory. Journal of Sound and Vibration. 1997, 208(2):271~287
5 Hyeung-Yun Kim, Woonbong Hwang. Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams. Composite Structures. 2002, 55 (1):51~62
6 L H Yam, Y J Yan, L Cheng, J S Jiang. Identification of complex crack damage for honeycomb sandwich plate using wavelet analysis and neural networks. Smart Materials and Structures. 2003, 12(5):661~671
7 陈昌亚, 宋汉文, 王德禹, 陶明德. 卫星结构铝蜂窝板非线性振动试验与参数辨识研究.振动与冲击. 2004,23(1):8~11
8 陈昌亚, 宋汉文, 王德禹, 陶明德. 卫星振动试验中固有频率“漂移"现象初步研究.振动与冲击. 2003,22(4):23~25
9 吴广玉. 系统辨识与自适应. 哈尔滨工业大学出版,1987:56~78
10 张成乾, 张国强. 系统辨识与参数估计. 机械工业出版社,1986:32~69
11 张洪锇, 胡干耀. 现代控制理论(第四册)系统辨识. 北京航空学院出版社,1987:41~80
12 方崇智, 萧德云. 过程辨识. 清华大学出版社, 1988:110~142
13 Merrill W. Identification of multivariable high performance turbofan engine dynamic from closed-loop data. J. Guidance. 1984,7(6):637~652
14 Peter Van O., Bart De M.. Subspace algorithms for the identification of combined deterministic-stochastic system. Automatics. 1994,30(1):75~93
15 马艳 , 曾庆福 , 李志舜 . 子空间辨识方法的改进 . 推进技术 . 2001,22(4):319~321
16 卜雄洙, 范茂军. 测试系统动态参数的时域辨识. 南京理工大学学报. 1995, 19(6):521~524
17 戎海武. 窄带随机噪声作用下强非线性系统的响应. 振动工程学报. 2003, 16(1):81~84
18 戎海武. 窄带随机噪声激励下多自由度非线性系统的响应. 力学季刊. 2003,24(2):211~218
19 赵玉成等. 时间序列关联维数在非线性系统运动性态识别中的应用. 航空学报. 2003,24(1):27~31
20 Motoda, Toshikazu, Miyazawa, Yoshikazu. Identification of influential uncertainties in Monte Carlo analysis. American Inst. Aeronautics and Astronautics Inc. 2002, 39(4):615~623
21 Nordlund P J , Fredrid G.. Sequential Monte Carlo filtering techniques applied to integrated navigation systems. IEEE Proceedings of the American Control Conference. 2001, (6):25~27
22 胡 荣 强 . 实 用 频 域 辨 识 方 法 的 讨 论 与 改 进 . 武 汉 工 学 院 学 报 . 1989,11(4):10~20
23 高 阳, 王三民, 刘晓宁. 一种改进的增量谐波平衡法及其在非线性振动中的应用. 机械科学与术. 2005,24(6):663~665
24 M. Thothandri, R. A. Casas, F. C. Moon, R. Dandrea, C. R. Johnson J.R.. Nonlinear System Identification of Multi-Degree-of-Freedom Systems. Nonlinear Dynamics. 2003, 32(3): 307~322
25 Miichael. A., Shcherbakov. Fast estimation of Wiener kernels of nonlinear systems in the frequency domain. IEEE Signal Processing Workshop on Higher-Order Statistics. 1997:117~121
26 张广莹, 邓正隆. 基于小波分析的非线性系统 Wiener 模型辨识.电机与控制学报. 2001,5(2):95~99
27 George-Othon A., Glentis, Panos Koukoulas, Nicholas Kalouptsidis. Efficient Algorithms for Volterra System Identification. IEEE Transactions on single processing. 1999, 47(11):3042~3057
28 Dorel Aiordachioaie. Detection and classification of non-linearities based on Volterra kernels processing. Engineering Applications of Artificial Intelligence. 2001, 14 (6):497~503
29 Animesh Chatterjeea, and Nalinaksh S, Vyas. Non-linear parameter estimation in multi-degree-of-freedom systems using multi-input Volterra series. Mechanical Systems and Signal Processing. 2004,18 (4):457~489
30 刘翀等. 基于非线性传递函数理论的非线性内模控制. 自动化技术与应用. 2000,19(5):1~4
31 欧文等. Volterra 泛函级数在非线性系统辨识中的应用. 控制与决策. 2002, 2(17): 239~242
32 Bendat, J. S.. Modern analysis procedures for multiple input/output problems. Journal of Sound and Vibration. 1980, 68(2): 498~512
33 Julius S. Bendat. 随机数据的非线性系统分析与辨识. 沈民奋等译. 西南交通大学出版社,1992:153~200
34 Julius S. Bendat. Robert N. Coppolino, Paul A. Palo. Identification of Physical Parameters with Memory in Non-Linear Systems. Int. J. Non-linear Mechanics. 1995,6(30):841~860
35 刘昆. 铝蜂窝夹层结构卫星频域非线性特性研究. 哈尔滨工业大学硕士论文.2004:9~32
36 王丽丽, 张景绘. 非线性动力学系统的辨识时频滤波与骨架曲线. 应用数学和力学. 2001,2(22):182~190
37 马宝萍, 徐志皋. 基于改进的 Elman 网络的内模控制及其应用. 热能动力工程. 2000, 15(4):429~431
38 魏民祥, 闫桂荣, 沈亚鹏. 基于动态神经网络非线性结构辨识的研究.应用力学学报. 2002,17(2):110~114
39 Billings, S. A. and etc. Properties of Neural Networks with Applications to Modeling Nonlinear Dynamical Systems. Int. J. Contro1. 1992,55(1):193~224
40 X. M. Ren, A. B. Rad, P. T. Chan, Wai Lun Lo. Identification and Control of Continuous-Time Nonlinear Systems via Dynamic Neural Networks. IEEE transactions on industrial electronics. 2003, 50(3):478~456
41 王文韬, 李成军, 田军. 基于一种改进BP神经网络的一类非线性系统辨识方法. 青岛科技大学学报. 2005,26(1):85~88
42 Thapa, B. K., Jones, B., Zhu, Q. M.. Non-linear control with neural networks. International Conference on Knowledge-Based Intelligent Electronic Systems, Proceedings. 2000: 868~873
43 Zhai Donghai, Li Li, Jin Fan. Nonlinear-Systems Model Identification withAdditive Multiplicative Fuzzy Neural Network. 电子科技大学学报. 2004, 33(5):577~581
44 Kosmatopoulos, E. B.. High-order neural network structures for identification of dynamical systems. Neural Networks. 1995, 6(2):422~431