部分输入未知条件下结构参数及激励识别
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摘要
针对部分输入未知条件下的结构参数和荷载识别问题,提出一种改进的基于最小二乘准则的自适应加权迭代算法。该方法通过引入自适应学习因子和加权正定矩阵,以任意假定的未知外激励作为初始迭代条件,以相邻两次迭代后荷载的识别值的误差作为收敛判断准则,有效地改进了迭代收敛速率、稳定性和识别精度。同时,针对比例阻尼,对现有非线性参数识别的松弛法进行改进,提出一种转换算法。通过一个具有15个自由度的高层数值模型的模拟数据和一个4层结构模型的动力试验实测数据分别验证了该方法有效性,同时,分别探讨了噪声水平、权重系数、学习因子等对算法收敛性的影响。数值算例和基于模型动力测试数据的识别结果表明,该算法具有稳定的收敛特性,参数和荷载识别精度高以及对测量噪声的鲁棒性强的特点。
The identification of structural parameters and dynamic loadings when partial inputs are unknown is important for damage detection and remaining service life forecasting of the structures.In this paper,an updated iterative identification approach,referred to as weighted adaptive iterative least-squares estimation with partially unknown inputs(WAILSE-PUI),was proposed to identify the structural parameters as well as the unknown external loadings simultaneously.In the proposed iteration approach,a learning coefficient using the information of the previous two iterations and a weighted positive definite matrix were employed for the purpose of improving the convergence of the identification approach.The initial values of the unknown external excitations were arbitrarily assumed and the iteration process would continue until the errors of the identifed external dynamic loadings of two adjacent iterations were within a pre-defined tolerance.Moreover,an approach to handling the Rayleigh damping which leads to nonlinear problems in the identification was proposed.The efficiency,accuracy,and robustness of the proposed method were validated via numerical simulation of a 15-degree-of-freedom high-rise building model and dynamic test of a four-story frame structure.The effect of noise level,weight,and learning coeficients on the convergence was discussed.Results show that the proposed approach can simulstanously identifiy structural parameters and unkown excitations with high accuracy,and is robust even with noise-polluted dynamic response measurements.
The identification of structural parameters and dynamic loadings when partial inputs are unknown is important for damage detection and remaining service life forecasting of the structures.In this paper,an updated iterative identification approach,referred to as weighted adaptive iterative least-squares estimation with partially unknown inputs(WAILSE-PUI),was proposed to identify the structural parameters as well as the unknown external loadings simultaneously.In the proposed iteration approach,a learning coefficient using the information of the previous two iterations and a weighted positive definite matrix were employed for the purpose of improving the convergence of the identification approach.The initial values of the unknown external excitations were arbitrarily assumed and the iteration process would continue until the errors of the identifed external dynamic loadings of two adjacent iterations were within a pre-defined tolerance.Moreover,an approach to handling the Rayleigh damping which leads to nonlinear problems in the identification was proposed.The efficiency,accuracy,and robustness of the proposed method were validated via numerical simulation of a 15-degree-of-freedom high-rise building model and dynamic test of a four-story frame structure.The effect of noise level,weight,and learning coeficients on the convergence was discussed.Results show that the proposed approach can simulstanously identifiy structural parameters and unkown excitations with high accuracy,and is robust even with noise-polluted dynamic response measurements.
引文
[1]Wu Z S,Xu B,Harada T.Review on structural healthmonitoring for infrastructure[J].Journal of AppliedMechanics,2003,6:1043-1054
[2]Norton J P.An introduction to identification[M].NewYork:Dover Publications,2009
[3]Farrar C R,Lieven N A J.Damage prognosis:the future ofstructural health monitoring[J].Philosophical Transactionsof the Royal Society A:Mathematical,Physical andEngineering Sciences,2007,365(1851):623-632
[4]Wang D,Haldar A.Element-level system identification withunknown input[J].Journal of Engineering Mechanics,1994,120(1):159-176
[5]Wang D,Haldar A.System identification with limitedobservations and without input[J].Journal of Engineering Mechanics,1997,123(5):504-511
[6]Zhao X,Xu Y L,Li J,et al.Hybrid identification methodfor multi-story buildings with unknown ground motion:theory[J].Journal of Sound and Vibration,2006,291(1/2):215-239
[7]Yang J N,Pan S,Lin S.Least-squares estimation withunknown excitations for damage identification of structures[J].Journal of Engineering Mechanics,2007,133(1):12-21
[8]Huang H,Yang J N,Zhou L.Adaptive quadratic sum-squares error with unknown inputs for damage identificationof structures[J].Structural Control and HealthMonitoring,2010,17(4):404-426
[9]Perry M J,Koh C G.Output-only structural identificationin time domain:numerical and experimental studies[J].Earthquake Engineering and Structural Dynamics,2008,37(4):517-533
[10]Sandesh S,Shankar K.Time domain identification ofstructural parameters and input time history using asubstructural approach[J].International Journal ofStructural Stability and Dynamics,2009,9(2):243-265
[11]Xu B,Wu Z,Yokoyama K,et al.A soft post-earthquakedamage identification methodology using vibration timeseries[J].Smart Materials and Structures,2005,14(3):116-124
[12]Xu Bin.Neural networks based structural model updatingmethodology using spatially incomplete accelerations[J].Lecture Notes in Computer Science,2006,4221:361-370
[13]陈隽,李杰.部分输入未知条件下的结构系统识别研究[J].地震工程与工程振动,1998,18(4):40-47(ChenJun,Li Jie.Study of structural system identification withincomplete input information[J].Earthquake Engineeringand Engineering Vibration,1998,18(4):40-47(inChinese))
[14]李杰,陈隽.结构参数未知条件下的地震动反演研究[J].地震工程与工程振动,1997,17(3):27-35(Li Jie,Chen Jun.Inversion of ground motion with unknownstructural parameters[J].Earthquake Engineering andEngineering Vibration,1997,17(3):27-35(in Chinese))
[15]李杰,陈隽.部分输入未知时求解动力复合反演问题的补偿算法[J].计算力学学报,2002,19(3):310-314(LiJie,Chen Jun.Compensation method for structuralparameter identification with incomplete input information[J].Chinese Journal of Computational Mechanics,2002,19(3):310-314(in Chinese))
[16]冯新,周晶,陈健云.一种结构参数识别的两阶段方法[J].计算力学学报,2002,19(2):222-227(Feng Xin,Zhou Jing,Chen Jianyun.A two-stage method foridentification of structural parameter[J].Chinese Journalof Computational Mechanics,2002,19(2):222-227(inChinese))
[17]陈健云,王建有.部分输入未知条件下结构参数识别法研究[J].计算力学学报,2005,22(2):149-154(ChenJianyun,Wang Jianyou.Study on identification method forstructural parameter with incomplete input information[J].Chinese Journal of Computational Mechanics,2005,22(2):149-154(in Chinese))
[18]谢献忠,易伟建.全量补偿复合反演算法的改进及其应用[J].工程力学,2005,22(1):28-32(Xie Xianzhong,Yi Weijian.Updated total compensation method for solvingcomposite inversion problem of structural dynamic system[J].Engineering Mechanics,2005,22(1):28-32(inChinese))
[19]陈隽,李杰.系统非线性参数识别的松驰法[J].振动工程学报,2001,14(4):447-450(Chen Jun,Li Jie.Arelaxation method for nonlinear system parameteridentification[J].Journal of Vibration Engineering,2001,14(4):447-450(in Chinese))
[20]Yang J N,Huang H.Sequential non-linear least-squareestimation for damage identification of structures withunknown inputs and unknown outputs[J].InternationalJournal of Non-Linear Mechanics,2007,42(5):789-801
[21]Peeters B,Van der Auweraer H,Guillaume P,et al.ThePolyMAX frequency-domain method:a new standard formodal parameter estimation[J].Shock and Vibration,2004,11(3/4):395-410
[2]Norton J P.An introduction to identification[M].NewYork:Dover Publications,2009
[3]Farrar C R,Lieven N A J.Damage prognosis:the future ofstructural health monitoring[J].Philosophical Transactionsof the Royal Society A:Mathematical,Physical andEngineering Sciences,2007,365(1851):623-632
[4]Wang D,Haldar A.Element-level system identification withunknown input[J].Journal of Engineering Mechanics,1994,120(1):159-176
[5]Wang D,Haldar A.System identification with limitedobservations and without input[J].Journal of Engineering Mechanics,1997,123(5):504-511
[6]Zhao X,Xu Y L,Li J,et al.Hybrid identification methodfor multi-story buildings with unknown ground motion:theory[J].Journal of Sound and Vibration,2006,291(1/2):215-239
[7]Yang J N,Pan S,Lin S.Least-squares estimation withunknown excitations for damage identification of structures[J].Journal of Engineering Mechanics,2007,133(1):12-21
[8]Huang H,Yang J N,Zhou L.Adaptive quadratic sum-squares error with unknown inputs for damage identificationof structures[J].Structural Control and HealthMonitoring,2010,17(4):404-426
[9]Perry M J,Koh C G.Output-only structural identificationin time domain:numerical and experimental studies[J].Earthquake Engineering and Structural Dynamics,2008,37(4):517-533
[10]Sandesh S,Shankar K.Time domain identification ofstructural parameters and input time history using asubstructural approach[J].International Journal ofStructural Stability and Dynamics,2009,9(2):243-265
[11]Xu B,Wu Z,Yokoyama K,et al.A soft post-earthquakedamage identification methodology using vibration timeseries[J].Smart Materials and Structures,2005,14(3):116-124
[12]Xu Bin.Neural networks based structural model updatingmethodology using spatially incomplete accelerations[J].Lecture Notes in Computer Science,2006,4221:361-370
[13]陈隽,李杰.部分输入未知条件下的结构系统识别研究[J].地震工程与工程振动,1998,18(4):40-47(ChenJun,Li Jie.Study of structural system identification withincomplete input information[J].Earthquake Engineeringand Engineering Vibration,1998,18(4):40-47(inChinese))
[14]李杰,陈隽.结构参数未知条件下的地震动反演研究[J].地震工程与工程振动,1997,17(3):27-35(Li Jie,Chen Jun.Inversion of ground motion with unknownstructural parameters[J].Earthquake Engineering andEngineering Vibration,1997,17(3):27-35(in Chinese))
[15]李杰,陈隽.部分输入未知时求解动力复合反演问题的补偿算法[J].计算力学学报,2002,19(3):310-314(LiJie,Chen Jun.Compensation method for structuralparameter identification with incomplete input information[J].Chinese Journal of Computational Mechanics,2002,19(3):310-314(in Chinese))
[16]冯新,周晶,陈健云.一种结构参数识别的两阶段方法[J].计算力学学报,2002,19(2):222-227(Feng Xin,Zhou Jing,Chen Jianyun.A two-stage method foridentification of structural parameter[J].Chinese Journalof Computational Mechanics,2002,19(2):222-227(inChinese))
[17]陈健云,王建有.部分输入未知条件下结构参数识别法研究[J].计算力学学报,2005,22(2):149-154(ChenJianyun,Wang Jianyou.Study on identification method forstructural parameter with incomplete input information[J].Chinese Journal of Computational Mechanics,2005,22(2):149-154(in Chinese))
[18]谢献忠,易伟建.全量补偿复合反演算法的改进及其应用[J].工程力学,2005,22(1):28-32(Xie Xianzhong,Yi Weijian.Updated total compensation method for solvingcomposite inversion problem of structural dynamic system[J].Engineering Mechanics,2005,22(1):28-32(inChinese))
[19]陈隽,李杰.系统非线性参数识别的松驰法[J].振动工程学报,2001,14(4):447-450(Chen Jun,Li Jie.Arelaxation method for nonlinear system parameteridentification[J].Journal of Vibration Engineering,2001,14(4):447-450(in Chinese))
[20]Yang J N,Huang H.Sequential non-linear least-squareestimation for damage identification of structures withunknown inputs and unknown outputs[J].InternationalJournal of Non-Linear Mechanics,2007,42(5):789-801
[21]Peeters B,Van der Auweraer H,Guillaume P,et al.ThePolyMAX frequency-domain method:a new standard formodal parameter estimation[J].Shock and Vibration,2004,11(3/4):395-410
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