結構損傷探測之試驗研究

Abstract

My thesis shows the recent advances in Numerical algorithms for Subspace State Space System IDentification (N4SID) and describes the reasons making this method attractive to the experiment on Damage Localization of Structures. The N4SID method is used for the identification of the linear time-invariant models in a state space from the input/output data. On the contrary to the other methods, it is based on the different principles, like the geometrical projections and numerical linear algebra. Therefore the stress is laid on the interpretations of this method in the well known frameworks of Kalman filter, Prediction error minimization and Instrumental variable methods. Recently N4SID algorithms, improvement and open problems are discussed and finally a new available research direction in subspace identification is presented. The new idea would allow to incorporate prior information into N4SID while recursifying the algorithm. In this thesis, I derive the N4SID algorithms to identify mixed deterministic-stochastic systems. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of non-steady state Kalman filter banks. From these it is easy to determine the state space system matrices. The N4SID algorithms are always convergent (non-iterative) and numerically stable since they only make use of QR and Singular Value Decompositions. In earthquake prone area, development of promising Structural Health Monitoring (SHM) systems to efficiently assess the integrity of critical structures right after the strike of an earthquake is desired. A deterministic-stochastic subspace identification method is adopted and experimentally verified in this thesis to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV) is then considered for damage detection. Members (or stories) with nearly zero stress under the static loadings of DLVs are considered potentially damaged, whereas the DLVs are derived from singular value decomposition of the flexibility differential of the structure before and after the damage state. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed.

My thesis shows the recent advances in Numerical algorithms for Subspace State Space System IDentification (N4SID) and describes the reasons making this method attractive to the experiment on Damage Localization of Structures. The N4SID method is used for the identification of the linear time-invariant models in a state space from the input/output data. On the contrary to the other methods, it is based on the different principles, like the geometrical projections and numerical linear algebra. Therefore the stress is laid on the interpretations of this method in the well known frameworks of Kalman filter, Prediction error minimization and Instrumental variable methods. Recently N4SID algorithms, improvement and open problems are discussed and finally a new available research direction in subspace identification is presented. The new idea would allow to incorporate prior information into N4SID while recursifying the algorithm. In this thesis, I derive the N4SID algorithms to identify mixed deterministic-stochastic systems. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of non-steady state Kalman filter banks. From these it is easy to determine the state space system matrices. The N4SID algorithms are always convergent (non-iterative) and numerically stable since they only make use of QR and Singular Value Decompositions. In earthquake prone area, development of promising Structural Health Monitoring (SHM) systems to efficiently assess the integrity of critical structures right after the strike of an earthquake is desired. A deterministic-stochastic subspace identification method is adopted and experimentally verified in this thesis to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV) is then considered for damage detection. Members (or stories) with nearly zero stress under the static loadings of DLVs are considered potentially damaged, whereas the DLVs are derived from singular value decomposition of the flexibility differential of the structure before and after the damage state. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed.