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Modal Identification and Damage Detection for Structural Health Monitoring Under Ambient Vibration Environment INTRODUCTION Recent developments in sensor technologies and research findings in vibration based structural health monitoring have made implementation of the health monitoring system in real-life structures feasible. Most of civil structures are under various ambient vibration environments such as traffic-, wind- and pedestrian-induced vibration, etc. Ambient vibration data measured for a certain duration (e.g. several days of periods) have an advantage of being inexpensive because no operational interference is needed to excite the structure and can be readily used for modal identification by output-only system identification techniques. For the modal identification, various techniques are currently available including the Eigensystem Realization Analysis (ERA) technique [Juang et al. 1985], Ibrahim Time Domain (ITD) method [Ibrahim et al. 1977] and Stochastic Subspace Iteration (SSI) technique [Van Overschee et al. 1996]. Recently, it has been known that the identified modal properties (e.g. natural frequency and damping ratio) are, to some extents, associated with the amplitudes of the ambient vibration in References [Nagayama et al. 2005, Siringoringo et al. 2008]. Nevertheless, there are few studies on the damping effects on the modal identification results by various identification techniques despite of inherent dependency of the damping on the amplitude [Fang et al. 1999]. Considering that increasing use of various damping devices and importance of condition monitoring of damaged or aged structures, studies of effects of the damping on the identified modal properties are on demand. On the other hand, the ambient vibration-based damage detection has received wide attentions in SHM research and practice community. 42490
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In 1997, Friswell et al. suggested a parameter subset selection method for use in locating damage. The method uses eigen-sensitivities, measuring the differences in natural frequencies between the damaged and undamaged states of a structure [Friswell et al. 1997]. Yun et al. suggested a new parameter subset selection method based on dynamic residual force measures which can accurately identify multiple damage locations [Yun et al. 2008a, Yun et al. 2008b]. The method was verified with incomplete dynamic measurements using a modal expansion method and effects of noise introduced in modal identification processes was investigated. However, the method has not been demonstrated for the ambient vibration-based damage detection. In this paper, a new health monitoring strategy has been suggested integrating NExT/ERA technique with a model based damage identification method. It consists of four major steps: 1) measurements of ambient vibration response; 2) modal identification using output-only techniques NExT/ERA in time domain; 3) damage localization using a new parameter subset selection method; 4) damage quantification formulated into optimization problems. Additionally, to distinguish physical true modes from non-physical comutational modes in the NExT/ERA technique, an improved consistency indicator that is better consistent in a wide range of damping ratios has been suggested through investigative parametric studies. A finite element model of a truss bridge structure has been built for numerical case studies. A series of numerical case studies with four different damage scenarios have been conducted under ambient vibration. Finally, the proposed methodology has shown potentials for either of damage diagnosis or finite model updating for model-based condition assessment of the remaining structural life. OUTPUT-ONLY MODAL IDENTIFICATION BY NEXT/ERA Natural Excitation Technique (NExT) Theoretical justification of the NExT technique is that correlation functions (auto- and cross-correlation functions) calculated from measured output data (commonly acceleration measurements) can be expressed in terms of sum of decaying sinusoids which have the same damped natural frequency and damping ratio as the impulse response function of the original structural system. NExT is based on the two assumptions: 1) input excitations are a stationary random white noise and uncorrelated with the response which is also a weakly stationary random process; 2) the structural system is excited within linear elastic regime so that the principle of superposition is valid. Details on its theoretical aspects can be found in References [Farrar et al. 1997, James et al. 1993]. To improve signals by reducing non-reproducible noise, ensemble averaging and windowing techniques are employed. Once impulse response of the system is obtained, ERA in the following section is used for modal identification. Eigensystem Realization Algorithm (ERA) In this section, the Eigensystem Realization Analysis (ERA) is briefly introduced. Details on the derivation can be referred to Reference [Juang et al. 1985, Juang 1994]. The ERA is originally based on Ho-Kalman procedure for realization of the space-state model of linear systems [Ho et al. 1965]. A finite-dimensional linear time-invariant system can be written in a state-space form as follows