基于ODS与随机子空间的模态分析研究
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摘要
模态分析是研究结构动力特性的一种近代方法,是系统识别方法在工程振动领域中的应用。模态是结构的固有振动特性,每一阶模态都具有特定的固有频率、阻尼比、振型、模态刚度和模态质量。这些模态可以由计算或试验分析取得,这样一个理论和实验的分析过程就称为模态分析。
本文依照实际工程的背景,对一个钢框架结构模型进行模态参数识别。首先,对钢框架结构建立有限元模型,并分析其动力特性,得到钢框架前10阶的固有频率和振型。然后,对该钢框架模型进行模态试验,试验通过力锤分别对钢框架进行随机敲击和单次敲击,通过传感器和数据采集系统得到结构的试验数据,再对试验数据进行后处理。
本文采用的参数识别方法是不测力法,即基于环境激励的模态参数识别方法。不测力法主要通过自己编写的MATLAB程序(响应谱分析法,随机子空间法)对试验数据进行处理。响应谱分析法是传统的识别方法,通过自谱、互谱图等来确定固有频率、阻尼比和振型。随机子空间(SSI)是一种比较先进的模态参数识别方法,但是传统的子空间识别方法是建立在有输入的基础之上。本文对该方法进行了改进,适用于无输入条件下的识别。
本文结论部分通过实验和理论的分析探讨了传统的参数识别方法和随机子空间参数识方法的一些问题,分析了不测力法在具体的结构的参数识别上的问题和误差大小。
Model analysis is the procedure of determining a structure’s dynamic characteristics recently , is a application of system identification method in vibration domain . Mode is structure’s inherence characteristics , each mode has specifically resonant frequencies , damping values , mode shapes, mode stiffness and mode mass. To obtain these modes , we can calculating and experimental analysis , such the course of theory and experimental analysis called Model analysis .
Based on the background of practical engineering , modal parameters identification of a steel frame structure in this paper . Fist , the dynamic character of the structure are analyzed by the Finite Element Model (FEM) obtain the low ten model resonant frequencies and model shapes . Then model experimental on the steel frame structure , experiment uses random knock and single knock separately on the steel frame structure through a force hammer . We can gained the data of experiment using transducers and the data acquisition system and post treatment of the data .
Modal parameters identification include ODS ,ODS mainly use MATLAB procedure(Response spectrum method , SSI) for dealing with the experiment data .Response spectrum method is using APS , CPS to identify modal parameters including resonant frequencies , damping and model shapes . Stochastic subspace identification(SSI) is a advanced modal parameters identification method , but traditional subspace parameters identification method based on having input data .
An improved method of stochastic subspace identification is given in this paper . The problems existing for structural model parameter identification , ODS and SSI in the conclusion of this paper .
本文依照实际工程的背景,对一个钢框架结构模型进行模态参数识别。首先,对钢框架结构建立有限元模型,并分析其动力特性,得到钢框架前10阶的固有频率和振型。然后,对该钢框架模型进行模态试验,试验通过力锤分别对钢框架进行随机敲击和单次敲击,通过传感器和数据采集系统得到结构的试验数据,再对试验数据进行后处理。
本文采用的参数识别方法是不测力法,即基于环境激励的模态参数识别方法。不测力法主要通过自己编写的MATLAB程序(响应谱分析法,随机子空间法)对试验数据进行处理。响应谱分析法是传统的识别方法,通过自谱、互谱图等来确定固有频率、阻尼比和振型。随机子空间(SSI)是一种比较先进的模态参数识别方法,但是传统的子空间识别方法是建立在有输入的基础之上。本文对该方法进行了改进,适用于无输入条件下的识别。
本文结论部分通过实验和理论的分析探讨了传统的参数识别方法和随机子空间参数识方法的一些问题,分析了不测力法在具体的结构的参数识别上的问题和误差大小。
Model analysis is the procedure of determining a structure’s dynamic characteristics recently , is a application of system identification method in vibration domain . Mode is structure’s inherence characteristics , each mode has specifically resonant frequencies , damping values , mode shapes, mode stiffness and mode mass. To obtain these modes , we can calculating and experimental analysis , such the course of theory and experimental analysis called Model analysis .
Based on the background of practical engineering , modal parameters identification of a steel frame structure in this paper . Fist , the dynamic character of the structure are analyzed by the Finite Element Model (FEM) obtain the low ten model resonant frequencies and model shapes . Then model experimental on the steel frame structure , experiment uses random knock and single knock separately on the steel frame structure through a force hammer . We can gained the data of experiment using transducers and the data acquisition system and post treatment of the data .
Modal parameters identification include ODS ,ODS mainly use MATLAB procedure(Response spectrum method , SSI) for dealing with the experiment data .Response spectrum method is using APS , CPS to identify modal parameters including resonant frequencies , damping and model shapes . Stochastic subspace identification(SSI) is a advanced modal parameters identification method , but traditional subspace parameters identification method based on having input data .
An improved method of stochastic subspace identification is given in this paper . The problems existing for structural model parameter identification , ODS and SSI in the conclusion of this paper .
引文
1 李德葆, 陆秋海. 试验模态分析及应用. 科学出版社, 2002:25~80
2 林循泓. 振动模态参数识别及其应用[M]. 南京, 东南大学出版社,1990:30~61
3 曹树谦等, 振动结构模态分析理论、实验与应用. 天津大学出版社, 2001:21~54
4 王柏生. 结构损伤检测与识别技术. 浙江大学出版社, 2001:55~78
5 Taehyoun Kim. Frequency-domain Karhunen-loeve method and its application to linear dynamic systems[J], AIAA Journal, 1990,2(2):2117~2123
6 高宝成等. 基于小波分析的简支梁裂缝识别方法研究, 振动工程学报,2003:1~7
7 费佩燕, 刘署光. 小波分析应用的进展和展望. 纺织高校基础科学学报, 2001:1~5
8 于开平等. 模态参数识别的小波变换方法. 宇航学报. 1999:1~12
9 李爱萍, 段利国. 小波分析在信号降噪处理中的应用. 太原理工大学学报. 2001:1~7
10 Ma.S..HHT. analysis of near-fied seismic ground motion [D]. Colorado School of Mines. 2003:1~8
11 黎洪生. 基于英特网的远程故障诊断技术与系统研究. 华中科技大学. 2003:1~9
12 Huang.H. and others. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-station time series analysis[J], 1998:124~220
13 Bremermann.H.J. Optimization. Through Evolution and Recombination Self-Oragnizing. Washington Spartan Books DC. 1996:534~556
14 Fogel.D.B.,Atmar,J.W. Comparing genetic operators with gaussian mutations in simulated evolutionary processes using linear systems. Biological Cybernetics. 2001:114~156
15 Fogel.D.B. System Identification Through Simulated Evolution: A Machine Learing Approach to Modeling. Gnnpress,Needham Heights MA, 2003:432~469
16 Dar-Yun. Chiang,Si-Tsong Huang .Modal parameter identification using simulated evolution. AIAA Journal. 1997:25~56
17 Taehyoun Kim. Frequency-domain Karhunen-loeve method and its application to linear dynamic systems[J]. AIAA Journal. 1998:342~373
18 Sirovich L, and others. An eigenfunction approach to large scale transitional structure is jet flow [J]. Physics of Fluids A. 1990:115~156
19 Breuer,K.S, Sirovich L. The use of the karhunen-loeve procedure for the calculation of linear eigenfunctions [J]. Journal of Computational Physics. 1991:687~810
20 Winter M, .and others. Eigenfunction ananlusis of turbulent mixing phenomena [J]. AIAA Journal. 1992:124~210
21 沃德.海伦, 斯蒂芬.拉门兹, 波尔.萨斯著. 白化同, 郭继重译. 屠良尧校. 模态分析理论和试验. 北京理工大学出版社. 2001:1~265
22 史东峰, 郑敏, 申凡, 鲍明. 工程结构工作模态的子空间识别法. 振动工程学报. 2002, 13(3):406~412
23 A.Berman F.S.Wei and K.V.Rao. Improvement of Analytical Dynastic Models Using Model Test. DataProc of the 21st SDM conf AIAA. 80-0800. 1900:345~398
24 王超, 李立, 陈绍汀. 结构振动有限元模型的精细修改方法. 西安交通大学学报. 1990, 24(S):1~8
25 曾庆华. 结构动力修改技术如干问题研究. 博士论文. 南京航天航空大学. 1998:23~54
26 R.J.Guyan. Reduction of Stiffness and Mass Matrix. AIAA Journal. 1965, 3(2):234~311
27 J.O Cauahan. A Procedure for Improved Reduced System. Model Proc of the 7th Internatinal Modal Analysis Conference. 1989:17-21
28 张德文. 结构动力分析中的逐级近似缩减法. 固体力学学报. 1994, 5(4):1~12
29 马宏伟, 杨桂通. 结构损伤探测的基本方法和研究进展. 1999, 29(4):98~527
30 周先雁, 沈蒲生, 程翔云. 用振动参数识别技术对混凝土框架进行损伤评估. 土木工程学报. 1998, 31(2):39~45
31 莱纳.荣著. 袁震东, 院荣耀, 陈树中译. 系统辨识、使用者的理论. 上海, 华东示范大学出版社. 1990:23~124
32 邹经湘, 屠良尧, 孔宪仁等编. 结构动力学哈尔滨工业大学出版社. 1996:43~287
33 H.G.. 纳特克著. 范宗喜, 吴祖玉译. 时间序列和模态分析的理论与实践导论. 电子工业出版社. 2002:76~134
34 T. 凯拉斯著 . 李清泉 , 褚家晋 , 高龙译 . 线性系统 . 科学出版社 . 1987:231~312
35 曹树谦, 张德文, 萧龙翔编著. 振动结构模态分析理论、实验与应用. 天津大学出版社. 2004:54~154
36 周传荣, M.Link. 修正结构有限元模型的一种方法. 振动工程学报. 1989, 2(4):1~11
37 Ibrahim S R. Computation of normal modes from identified complex modes. AIAA. 1992, 21(3):44~47
38 M I Friswell and J E Mottershead. Finite element model updating in structural dynamics. Kluwer Acadamic Publishers. 2005:213~342
39 M.Lee and M.Richardson. Subspace-based Methods for the Identification of Liner Time-invariant System. Automatica. 1995, V,31(12):835~1851
40 W.Favoreel B.de Moor and P.Van overschee. Subspace State Space System Identification for Indutrial Processess ,in Proc of the 5th IFAC Symposium on Dunamics and Control of Process systems Corfu, Greece. 1998, pp:322~330
41 J.S Lew, J.N.Juang and R.W.Longman. Comparision of severl System Identification Methods for Flexible Structure. Journal of socend and vibration. 1993, V.167, pp:461~480
2 林循泓. 振动模态参数识别及其应用[M]. 南京, 东南大学出版社,1990:30~61
3 曹树谦等, 振动结构模态分析理论、实验与应用. 天津大学出版社, 2001:21~54
4 王柏生. 结构损伤检测与识别技术. 浙江大学出版社, 2001:55~78
5 Taehyoun Kim. Frequency-domain Karhunen-loeve method and its application to linear dynamic systems[J], AIAA Journal, 1990,2(2):2117~2123
6 高宝成等. 基于小波分析的简支梁裂缝识别方法研究, 振动工程学报,2003:1~7
7 费佩燕, 刘署光. 小波分析应用的进展和展望. 纺织高校基础科学学报, 2001:1~5
8 于开平等. 模态参数识别的小波变换方法. 宇航学报. 1999:1~12
9 李爱萍, 段利国. 小波分析在信号降噪处理中的应用. 太原理工大学学报. 2001:1~7
10 Ma.S..HHT. analysis of near-fied seismic ground motion [D]. Colorado School of Mines. 2003:1~8
11 黎洪生. 基于英特网的远程故障诊断技术与系统研究. 华中科技大学. 2003:1~9
12 Huang.H. and others. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-station time series analysis[J], 1998:124~220
13 Bremermann.H.J. Optimization. Through Evolution and Recombination Self-Oragnizing. Washington Spartan Books DC. 1996:534~556
14 Fogel.D.B.,Atmar,J.W. Comparing genetic operators with gaussian mutations in simulated evolutionary processes using linear systems. Biological Cybernetics. 2001:114~156
15 Fogel.D.B. System Identification Through Simulated Evolution: A Machine Learing Approach to Modeling. Gnnpress,Needham Heights MA, 2003:432~469
16 Dar-Yun. Chiang,Si-Tsong Huang .Modal parameter identification using simulated evolution. AIAA Journal. 1997:25~56
17 Taehyoun Kim. Frequency-domain Karhunen-loeve method and its application to linear dynamic systems[J]. AIAA Journal. 1998:342~373
18 Sirovich L, and others. An eigenfunction approach to large scale transitional structure is jet flow [J]. Physics of Fluids A. 1990:115~156
19 Breuer,K.S, Sirovich L. The use of the karhunen-loeve procedure for the calculation of linear eigenfunctions [J]. Journal of Computational Physics. 1991:687~810
20 Winter M, .and others. Eigenfunction ananlusis of turbulent mixing phenomena [J]. AIAA Journal. 1992:124~210
21 沃德.海伦, 斯蒂芬.拉门兹, 波尔.萨斯著. 白化同, 郭继重译. 屠良尧校. 模态分析理论和试验. 北京理工大学出版社. 2001:1~265
22 史东峰, 郑敏, 申凡, 鲍明. 工程结构工作模态的子空间识别法. 振动工程学报. 2002, 13(3):406~412
23 A.Berman F.S.Wei and K.V.Rao. Improvement of Analytical Dynastic Models Using Model Test. DataProc of the 21st SDM conf AIAA. 80-0800. 1900:345~398
24 王超, 李立, 陈绍汀. 结构振动有限元模型的精细修改方法. 西安交通大学学报. 1990, 24(S):1~8
25 曾庆华. 结构动力修改技术如干问题研究. 博士论文. 南京航天航空大学. 1998:23~54
26 R.J.Guyan. Reduction of Stiffness and Mass Matrix. AIAA Journal. 1965, 3(2):234~311
27 J.O Cauahan. A Procedure for Improved Reduced System. Model Proc of the 7th Internatinal Modal Analysis Conference. 1989:17-21
28 张德文. 结构动力分析中的逐级近似缩减法. 固体力学学报. 1994, 5(4):1~12
29 马宏伟, 杨桂通. 结构损伤探测的基本方法和研究进展. 1999, 29(4):98~527
30 周先雁, 沈蒲生, 程翔云. 用振动参数识别技术对混凝土框架进行损伤评估. 土木工程学报. 1998, 31(2):39~45
31 莱纳.荣著. 袁震东, 院荣耀, 陈树中译. 系统辨识、使用者的理论. 上海, 华东示范大学出版社. 1990:23~124
32 邹经湘, 屠良尧, 孔宪仁等编. 结构动力学哈尔滨工业大学出版社. 1996:43~287
33 H.G.. 纳特克著. 范宗喜, 吴祖玉译. 时间序列和模态分析的理论与实践导论. 电子工业出版社. 2002:76~134
34 T. 凯拉斯著 . 李清泉 , 褚家晋 , 高龙译 . 线性系统 . 科学出版社 . 1987:231~312
35 曹树谦, 张德文, 萧龙翔编著. 振动结构模态分析理论、实验与应用. 天津大学出版社. 2004:54~154
36 周传荣, M.Link. 修正结构有限元模型的一种方法. 振动工程学报. 1989, 2(4):1~11
37 Ibrahim S R. Computation of normal modes from identified complex modes. AIAA. 1992, 21(3):44~47
38 M I Friswell and J E Mottershead. Finite element model updating in structural dynamics. Kluwer Acadamic Publishers. 2005:213~342
39 M.Lee and M.Richardson. Subspace-based Methods for the Identification of Liner Time-invariant System. Automatica. 1995, V,31(12):835~1851
40 W.Favoreel B.de Moor and P.Van overschee. Subspace State Space System Identification for Indutrial Processess ,in Proc of the 5th IFAC Symposium on Dunamics and Control of Process systems Corfu, Greece. 1998, pp:322~330
41 J.S Lew, J.N.Juang and R.W.Longman. Comparision of severl System Identification Methods for Flexible Structure. Journal of socend and vibration. 1993, V.167, pp:461~480