确定子空间识别方法在桥梁振动台模型试验中的对比
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摘要
为了探讨确定子空间识别(DSI)方法与确定-随机子空间识别(CDSI)方法在实际应用中的性能,开展了DSI方法与CDSI方法的对比研究。首先,对DSI方法与CDSI方法的算法原理进行介绍,对比了过程噪声和测试噪声在2种方法中不同的考虑方式,分析了CDSI方法在算法层面的优势。以大比尺斜拉桥模型振动台试验为依托,获取模型桥在4种不同强度等级的集集(Chichi)地震动激励下的加速度响应,为考察DSI方法与CDSI方法的算法性能提供数据支撑。然后,分别使用DSI方法与CDSI方法对模型桥的模态参数进行识别,使用稳定图对模态参数识别结果进行展示,并统计了图中稳定点个数,对比2种方法模态参数识别结果的稳定性。最后,对DSI方法与CDSI方法的振型识别结果进行展示,并统计2种方法的振型模态置信准则值(MAC),对比了2种方法振型识别结果的差异。结果表明:DSI方法与CDSI方法识别得到的频率与阻尼比基本一致,但CDSI方法识别结果的稳定性略优;DSI方法比CDSI方法识别得到的振型幅值略大,经量纲一化处理后,2种方法识别的振型形状基本一致,但随着模态阶次的增高和激励强度的增强,两者振型的差异逐渐增大;CDSI方法考虑了数据中的过程噪声和测试噪声,其模态参数识别结果的稳定性略优于DSI方法,但同时其也降低了CDSI方法的计算效率,CDSI方法的优势并不是压倒性的。
In order to investigate the performance of the deterministic subspace identification(DSI) and the combined deterministic-stochastic subspace identification(CDSI) in practical applications, a comparison study of DSI and CDSI were carried out. First, the algorithm principles of DSI and CDSI were introduced, the different ways of considering the process noise and measurement noise were compared, and the advantages in the algorithm of CDSI were discussed. Next, a shaking table test of a large-scale cable-stayed bridge model was used as a case study, the acceleration responses of the model bridge under four different degrees of Chichi seismic excitation were obtained, and data were prepared for investigating the performance of DSI and CDSI. Then, the DSI and CDSI were conducted to identify the modal parameters of the model bridge. A stabilization diagram was used to present the modal parameter identification results and the number of stabilization points was counted, the stability of the identification results of the two methods were compared. Finally, the mode shape identification results of DSI and CDSI were exhibited and the modal assurance criterions(MAC) between their mode shapes were calculated, and the differences of the mode shape identification results of the two methods were compared. The results show that the identification results of frequency and damping ratio of DSI and CDSI are consistent, however, the identification results of CDSI possess a higher stability. The amplitudes of mode shapes of DSI are slightly greater than those of CDSI, and the amplitude of the mode shapes of the two methods are approximately the same after normalization processing. However, the difference between the mode shapes of the two methods increases with the increase of the mode order and excitation degree. Process noise and measurement noise are considered in CDSI, and its modal parameter identification results are slightly better than those of DSI. However, considering noise reduces the computational efficiency of CDSI, and thus, the advantages of CDSI do not seem significant. 2 tabs, 12 figs, 25 refs.
In order to investigate the performance of the deterministic subspace identification(DSI) and the combined deterministic-stochastic subspace identification(CDSI) in practical applications, a comparison study of DSI and CDSI were carried out. First, the algorithm principles of DSI and CDSI were introduced, the different ways of considering the process noise and measurement noise were compared, and the advantages in the algorithm of CDSI were discussed. Next, a shaking table test of a large-scale cable-stayed bridge model was used as a case study, the acceleration responses of the model bridge under four different degrees of Chichi seismic excitation were obtained, and data were prepared for investigating the performance of DSI and CDSI. Then, the DSI and CDSI were conducted to identify the modal parameters of the model bridge. A stabilization diagram was used to present the modal parameter identification results and the number of stabilization points was counted, the stability of the identification results of the two methods were compared. Finally, the mode shape identification results of DSI and CDSI were exhibited and the modal assurance criterions(MAC) between their mode shapes were calculated, and the differences of the mode shape identification results of the two methods were compared. The results show that the identification results of frequency and damping ratio of DSI and CDSI are consistent, however, the identification results of CDSI possess a higher stability. The amplitudes of mode shapes of DSI are slightly greater than those of CDSI, and the amplitude of the mode shapes of the two methods are approximately the same after normalization processing. However, the difference between the mode shapes of the two methods increases with the increase of the mode order and excitation degree. Process noise and measurement noise are considered in CDSI, and its modal parameter identification results are slightly better than those of DSI. However, considering noise reduces the computational efficiency of CDSI, and thus, the advantages of CDSI do not seem significant. 2 tabs, 12 figs, 25 refs.
引文
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[24] 常军,张启伟,孙利民.稳定图方法在随机子空间识别模态参数中的应用[J].工程力学,2007,24(2):39-44.CHANG Jun,ZHANG Qi-wei,SUN Li-min.Application of stabilization diagram for modal parameter identification using stochastic subspace method[J].Engineering Mechanics,2007,24(2):39-44.
[25] LEI S,MAO K,LI L,et al.Sensitivity analysis of modal assurance criteria of damped systems[J].Journal of Vibration and Control,2017,23(4):632-644.
[2] 房贞政,张超,陈永健,等.基于三台阵振动台的多塔斜拉桥试验研究[J].土木工程学报,2012,45(增1):25-29.FANG Zhen-zheng,ZHANG Chao,CHEN Yong-jian,et al.Research on the shaking table test of three towers cable-stayed bridge based on three shaking table system[J].China Civil Engineering Journal,2012,45 (S1):25-29.
[3] 柳春光,孙国帅,张士博,等.深水桩墩结构振动台试验及地震响应预测分析[J].大连理工大学学报,2013,53(1):114-120.LIU Chun-guang,SUN Guo-shuai,ZHANG Shi-bo,et al.Experimental investigation of shaking table on pile-pier structure in deep water and prediction analysis of seismic response[J].Journal of Dalian University of Technology,2013,53(1):114-120.
[4] 王瑞龙,徐艳,李建中.一致激励下的混凝土斜拉桥振动台试验[J].同济大学学报:自然科学版,2015,43(3):357-363.WANG Rui-long,XU Yan,LI Jian-zhong.Shake table test of a concrete cable-stayed bridge subjected to uniform seismic excitation[J].Journal of Tongji University:Natural Science,2015,43(3):357-363.
[5] 孙利民,谢文.超大跨斜拉桥多点振动台试验研究[J].工程力学,2016,33(11):38-48.SUN Li-min,XIE Wen.Experimental studies on super long-span cable-stayed bridge by using multiple shake table testing[J].Engineering Mechanics,2016,33(11):38-48.
[6] 徐艳,王瑞龙,李建中,等.弹塑性钢阻尼器对中等跨径斜拉桥横桥向减震效果的振动台试验研究[J].工程力学,2016,33(8):101-109.XU Yan,WANG Rui-long,LI Jian-zhong,et al.Shaking table test of transverse seismic response reduction of medium-span cable-stayed bridges using yielding steel dampers[J].Engineering Mechanics,2016,33(8):101-109.
[7] 李勇,闫维明,刘晶波,等.近断层高架连续梁桥地震易损性与振动台试验研究[J].工程力学,2018,35(4):52-60,86.LI Yong,YAN Wei-ming,LIU Jing-bo,et al.Seismic vulnerability analysis and a shaking table test of a near-fault continuous viaduct[J].Engineering Mechanics,2018,35(4):52-60,86.
[8] 单德山,周筱航,杨景超,等.结合地震易损性分析的桥梁地震损伤识别[J].振动与冲击,2017,36(16):195-201.SHAN De-shan,ZHOU Xiao-hang,YANG Jing-chao,et al.Bridge seismic damage identification based on seismic fragility analysis[J].Journal of Vibration and Shock,2017,36(16):195-201.
[9] DE JONG P.Smoothing and interpolation with the state-space model[J].Journal of the American Statistical Association,1989,84(408):1085-1088.
[10] VAN OVERSCHEE P,DE MOOR B.Subspace identification for linear systems:Theory-implementation-applications[M].Boston:Kluwer Academic Publisher,2012.
[11] VAN OVERSCHEE P,DE MOOR B.Subspace identification[J].International Journal of Control,1995,78(17):1412-1436.
[12] BORJAS S D M,GARCIA C.Subspace identification for industrial processes[J].TEMA (Sao Paulo),2011,12(3):183-194.
[13] 单德山,李乔,付春雨,等.智能桥梁健康监测与损伤评估[M].北京:人民交通出版社,2010.SHAN De-shan,LI Qiao,FU Chun-yu,et al.Intelligent bridge health monitoring and damage assessment[M].Beijing:China Communications Press,2010.
[14] KURKA P R G,CAMBRAIA H N.Application of a multivariable input-output subspace identification technique in structural analysis[J].Journal of Sound and Vibration,2008,312(3):461-475.
[15] KURKA P R G,BRAUN S.Direct multivariate subspace time identification[J].Mechanical Systems and Signal Processing,2010,24(6):1634-1645.
[16] BAKIR P G.The combined deterministic stochastic subspace based system identification in buildings[J].Structural Engineering & Mechanics,2011,38(3):315-332.
[17] MOAVENI B,ASGARIEH E.Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems[J].Mechanical Systems and Signal Processing,2012,31:40-55.
[18] BELLERI A,MOAVENI B,RESTREPO J I.Damage assessment through structural identification of a three-story large-scale precast concrete structure[J].Earthquake Engineering & Structural Dynamics,2014,43(1):61-76.
[19] D′AMORE E,AMADDEO C,ASTANEH A A.Health monitoring of an instrumented SRMF building using earthquake data[J].The Structural Design of Tall and Special Buildings,2014,23(13):980-994.
[20] HUANG M C,WANG Y P,CHANG M L.Damage detection of structures identified with deterministic-stochastic models using seismic data[J/OL].The Scientific World Journal,2014:1-14[2014-08-03].http://dx.doi.org/10.1155/2014/879341.
[21] MOAVENI B,STAVRIDIS A,LOMBAERT G,et al.Finite-element model updating for assessment of progressive damage in a 3-story infilled RC frame[J].Journal of Structural Engineering,2012,139(10):1665-1674.
[22] ABDELGHANI M,VERHAEGEN M,VAN OVERSCHEE P,et al.Comparison study of subspace identification methods applied to flexible structures[J].Mechanical Systems and Signal Processing,1998,12(5):679-692.
[23] MRABET E,ABDELGHANI M,KAHLA N B.A new criterion for the stabilization diagram used with stochastic subspace identification methods:An application to an aircraft skeleton[J/OL].Shock and Vibration,2014:1-8[2014-04-17].http://dx.doi.org/10.1155/2014/409298.
[24] 常军,张启伟,孙利民.稳定图方法在随机子空间识别模态参数中的应用[J].工程力学,2007,24(2):39-44.CHANG Jun,ZHANG Qi-wei,SUN Li-min.Application of stabilization diagram for modal parameter identification using stochastic subspace method[J].Engineering Mechanics,2007,24(2):39-44.
[25] LEI S,MAO K,LI L,et al.Sensitivity analysis of modal assurance criteria of damped systems[J].Journal of Vibration and Control,2017,23(4):632-644.