||Study on Recursive Subspace Identification of State-Space Models
||Department of Civil Engineering
Recursive subspace identification
Finite element model
The purpose of this thesis is to apply the multivariable recursive subspace identification (RSI) algorithm to the computer-aided analysis program. By obtaining the acceleration responses of the finite element models during earthquake excitation as input and output data for system identification to continuously identify the system parameters through recursive algorithm. The identified system parameters and the known system mass matrix are used to estimate the stiffness matrix of the system, and compare the identification and estimation results with that computed by the finite element model to verify the accuracy and applicability of this system identification method.
In this thesis, several finite element models with different shapes and degrees of freedom are established, and artificial earthquakes with different peak ground accelerations (PGA) and different dominant periods (Ts) are applied. The RSI method is used to continuously identify the system parameters of these simulation cases during seismic excitation. In addition, in reality, the effect of noise on acceleration measurement must be considered, so white noise with different noise-to-signal ratios is applied to simulate the influence of the noise on system identification, and the tolerance of noise of RSI method can be known.
The results of this thesis indicate that this RSI method can obtain good identified results in various structural models, and under different types of earthquake excitations. In addition, it also shows that the RSI method can maintain respectable identification results when the amplitude of the noise is not too large. Note that the computer-aided analysis programs in this thesis are developed by Shen-Haw Ju’s research team, which are free to use.
List of Tables VII
List of Figures X
Chapter 1 Introduction 1
1.1 Background and research purposes 1
1.2 Literature Review 2
1.2.1 Research correlated to system identification 2
1.2.2 Research correlated to model order reduction and model correction method 4
1.2.3 Research correlated to control algorithms of ATMD 5
1.3 Overview 6
Chapter 2 Research Theories and Methods 7
2.1 State-Space Modeling of a Structure 7
2.1.1 Continuous-time state-space model 7
2.1.2 Discrete-time state-space model 8
2.2 Subspace Identification for Modal Analysis 9
2.2.1 Data organization 10
2.2.2 Estimation of the extended observability matrix 12
2.3 Recursive Subspace Identification 17
2.4 Model order reduction of finite element models 22
2.4.1 Guyan reduction (Static condensation) 22
2.4.2 Improved Reduction System (IRS) method 23
2.5 Suggestion for User-defined Parameters 25
Chapter 3 Simulation Programs and Operating Procedures 27
3.1 Relevant Programs for Finite Element Models 27
3.1.1 Description of relevant programs 27
3.1.2 Operating procedures for finite element model 28
3.2 Generation of Artificial Earthquakes 38
3.3 Recursive Subspace System Identification Procedure 41
3.3.1 Operating procedure of RSI programs 43
Chapter 4 Simulation Study 44
4.1 System Identification of Different Models Under Same Artificial Earthquake Excitation 44
4.1.1 Model description 44
4.1.2 System identification results 45
4.2.1 The Model Under Artificial Earthquakes with Different Ts 68
4.2.2 The Model Under Artificial Earthquakes with Different PGA 70
4.3 Modal Identification of Models with White Noise 72
4.4 System Identification of Several Special Models 86
Chapter 5 Result and Discussion 96
5.1 Discussion of General Shape Model Cases 96
5.2 Discussion of Models Under Different Earthquakes 98
5.3 Discussion of Models Consider Measured White Noise 99
5.4 Discussion of Several Special Model Cases 100
Chapter 6 Conclusions and Future Work 102
6.1 Conclusions 102
6.2 Future Work 104
6.2.1 Equations of motion of an active control system 104
6.2.2 LQR control method 105
Appendix A 111
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