@phdthesis{oai:sucra.repo.nii.ac.jp:00017935,
 author = {SAMIM, MUSTAFA},
 month = {},
 note = {xx, 95 p., The existing infrastructure such as bridges which are the valuable national assets for transportation and economy are required to be maintained properly to ensure the performance and condition for their continuous operation. Difficulties in practical application of vibration-based structural health monitoring (SHM) of structures include considerable amount of uncertainties in structural modeling and vibration measurement and sensitivity issues of modal parameters due to local damage in case of large structure. This dissertation proposed an analytical framework for SHM addressing the aforementioned difficulties by combining two techniques: A Bayesian based probabilistic approach for finite element model (FE-model) updating that accounts for the underlying uncertainties and an energy-based damping model for detecting damage at local level using a small number of sensors.
An efficient and robust Bayesian model updating was presented in this dissertation by introducing a new objective function and a realistic parameterization of mass and stiffness matrices. In this framework, the likelihood function for mode shapes was formulated based on the cosine of the angle between the analytical and measured mode shapes which does not require any scaling or normalization as compared to conventional Bayesian methods. Four stiffness parameters were introduced for each element considering both sectional and material properties to take into account variation in each element due to local damage. The proposed updating method was validated experimentally by updating a FE-model of existing steel truss bridge utilizing the vibration data obtained from limited number of sensors by a car running test.
It has been recognized that the damping is more sensitive to local damage and the advantage of using damping is that the damping change in global modes affected by local damage can be identified with a small number of sensors. In this dissertation, an energy-based damping model was introduced for practical and effective SHM by estimating the contribution of modal damping ratios from different structural elements utilizing the data from updated FE-model and the identification results of damping from a small number of sensors. A previous study reported that the studied bridge with damage at local diagonal member showed a significant increase in the damping of global vibration mode of the structure. The present study utilized the energy-based damping evaluation to identify possible cause of the modal damping increase by observing the change in the contribution from different structural elements on the modal damping ratios., Title Page　i
Acknowledgement　v
Abstract　vii
Table of Contents　ix
List of Figures　xiii
List of Tables　xv
Nomenclature　xvii
Abbreviations　xix
CHAPTER 1　INTRODUCTION　1
1.1　Research Background and Motivation　1
1.2　Objectives of the Study　3
1.3　Outline of the Dissertation　4
CHAPTER 2　LITERATURE REVIEW　7
2.1　An Overview of Vibration-based Structural Health Monitoring　7
2.2　Vibration-based Structural Health Monitoring Techniques　9
　2.2.1　Non-model based Methods　9
　2.2.2　Model-based Inverse Methods　10
2.3　Difficulties in Practical Application of Vibration-based SHM　12
　2.3.1　Issues with Sensing and System Identification　13
　2.3.2　Issues with Model-based SHM　14
　2.3.3　Issues with Sensitivity of Modal Parameters to Local Damage　15
2.4　Proposed Framework to Overcome Aforementioned Difficulties　15
CHAPTER 3　BAYESIAN PROBABILISTIC APPROACH FOR MODEL UPDATING USING LIMITED SENSOR DATA　19
3.1　Introduction　19
3.2　Application of Bayesian Probabilistic Approach to FE-model Updating　19
　3.2.1　Bayesian Probabilistic Approach　19
　3.2.2　Parameterization of Mass and Stiffness Matrices　20
　3.2.3　Formulation of Likelihood Function　20
　3.2.4　Formulation of Eigenvalue Equation Errors　22
　3.2.5　Formulation of Prior PDF　22
　3.2.6　Formulation of Posterior PDF　23
3.3　Optimal Parameter Vectors　23
　3.3.1　Optimization for Auxiliary Variables and Lagrange Multipliers　24
　3.3.2　Optimization for Mode Shape Vectors　24
　3.3.3　Optimization for Frequencies　24
　3.3.4　Optimization for Stiffness Parameters　24
　3.3.5　Optimization for Mass Parameters　25
3.4　Studied Steel Truss Bridge　25
　3.4.1　Test Structure Description　25
　3.4.2　Finite Element Model of Test Structure　25
3.5　Experimental Validation of Proposed Updating Framework　27
　3.5.1　Vibration Measurements and System Identification　27
　3.5.2　Parameterization of Mass and Stiffness Matrices for the Truss Bridge　30
　3.5.3　Model Updating Results and Discussion　31
3.6　Conclusions　34
CHAPTER 4　ENERGY-BASED DAMPING EVALUATION FOR SHM　37
4.1　Introduction　37
4.2　Energy-based Damping Evaluation　37
　4.2.1　Energy-based Damping Model for Test Bridge　38
　4.2.2　Elemental Damping Evaluation　40
　4.2.3　Evaluation of Modal Energies　40
4.3　Application to Test Bridge　41
　4.3.1　Experimental Damping Identification　41
　4.3.2　Identification of Loss Factors and Friction Coefficients　42
　4.3.3　Evaluation of Analytical Modal Damping Ratios　44
　4.3.4　Contribution of Modal Damping from Each Element　47
4.4　Conclusions　48
CHAPTER 5　APPLICATION OF PROPOSED FRAMEWORK TO SHM WITH A SMALL NUMBER OF SENSORS　51
5.1　Introduction　51
5.2　Problem Description　51
5.3　Identification of Loss Factors for Damaged Span　54
5.4　Damage Detection Using Change in Analytical Modal Damping Ratios　55
　5.4.1　Evaluation of Analytical Modal Ratios for Damaged Span　55
　5.4.2　Re-analysis of Loss Factors for Damaged Span　57
　5.4.3　Justification Against Change in Loss Factors and Discussion　58
5.5　Conclusions　62
CHAPTER 6　SUMMARY AND FUTURE WORKS　63
6.1　Summary of the Contribution Made　63
6.2　Suggestions for Further Work　65
REFERENCES　68
APPENDIX A　OPTIMAL SENSOR PLACEMENT FOR AN EXISTING STEEL TRUSS BRIDGE　73
A.1　Introduction　73
A.2　OSP Techniques　73
　A.2.1　Effective Independence Method　74
　A.2.2　Energy Matrix Rank Optimization　75
　A.2.3　Modal Approach Using System Norms　76
A.3　Results of OSP for Test Structure　77
A.4　Conclusions　78
References　79
APPENDIX B　DAMAGE DETECTION BY FE-MODEL UPDATING　81
B.1　Application to SHM　81
B.2　Damage Detection　82
　B.2.1　Considering Simulated Damage　82
　B.2.2　Considering Experimental Data from Damaged Span　85
B.3　Conclusions　88
APPENDIX C　FORMULATION AND PARAMETERIZATION OF MASS AND STIFFNESS MATRICES　91
C.1　Stiffness Formulation　91
C.2　Mass Formulation　92
C.3　Transformation of Coordinates　93
C.4　Parameterization of Mass and Stiffness Matrices　94, 主指導教員 : 松本泰尚, text, application/pdf},
 school = {埼玉大学},
 title = {AN ENERGY-BASED DAMPING EVALUATION USING BAYESIAN MODEL UPDATING FOR VIBRATION-BASED STRUCTURAL HEALTH MONITORING OF STEEL TRUSS BRIDGES},
 year = {2017},
 yomi = {サミン, ムスタファ}
}