研 究 生:吳艾倫
The purpose of structural health monitoring is to detect the occurrence of damage on structure for examining the damage extension and even damage location and system identification technique is one of the tool for the structural health monitoring. Generally, there are two different methods in system identification: one is parametric identification and the other is the nonparametric identification, where the former involves the comparison of the changes in structural properties or response, where appropriate interpretation of the change in structural properties or response due to damage is a critical task. In the case of parametric identification, deterioration or damage of structure is usually described as the decrease in structural parameters. Identifications on the changes in the dynamic properties such as natural frequency and mode shapes have been widely studied, which use mathematical models to describe structural behavior and establish mathematical model to approximate the relationship between the specific damage condition and changes in structural response. However, the drawbacks of this parametric identification using
mathematical-model-based method are computationally expensive and tend to be numerically unstable for large-scale infrastructure.
From another point of view of L.H.Lee et al. (1999), the embedded statistical model of reduction factor had been established by calibrating the reference-based model with considering
different hysteretic characteristics independently. This concept truly provides a suggestion on computational efficiency on the estimation of seismic demands. This embedded model can be extended to different type of seismic demands which is in relating to structural damage characteristics. Through the observation on the effect of different hysteretic behaviors with respect to reference-based model the damage can be quantified. Hence, a damage diagnosis methodology is proposed which includes two parts: First system identification is used to identify the model parameters of analytical hysteretic model from measurement. Second, through the embedded statistical model, one can observe the effect of different hysteretic behaviors using the proposed reference-based model and even predict the indices of seismic demand which have strong relation to damage indices and quantify the degree of damage.
Reference-based Statistical Model
The procedure for developing the statistical model for structural damage diagnosis is introduced. A benchmark hysteretic model will be selected in the first place. This model was developed based on the cyclic loading test data of a rectangular column which was designed according to the new Taiwan Seismic Design Code [NCREE-99-030]. The hysteretic model parameters from the restoring force diagram of this selected specimen are identified. A generalized bilinear model will be proposed through modification on those identified parameters which will be defined as the reference-based inelastic hysteretic model. Then, response indices will be calculated by conducting the dynamic analysis of the nonlinear SDOF system implemented with the reference-based inelastic hysteretic model subject to input ground excitation. Through statistical analysis, the seismic demand indices can be calculated and represented as functions of system natural period and ductility ratios. Therefore, a reference-based model with different response indices are established.
Second, variability of the hysteretic characteristics is taking into consideration. Since different
hysteretic model will control the post yielding, stiffness, strength and the pinching effects, then response indices of the variability of hysteretic model parameters can be developed. Comparison on these indices with those obtained from the reference-based model is made. Embedded statistical model will be determined by calibrating the reference-base model as function of not only system natural period, ductility ratios, but also model parameters considering different hysteretic behaviors.
Inelastic Deteriorating Hysteretic Model
Structures subjected to strong earthquake excitations are expected to exhibit hysteretic behavior and dissipate energy through inelastic material behavior. To verify the seismic performance of structures requires non-linear analytical analysis and the most difficulties come from the lacking information of inelastic properties of structures. To overcome the difficulties, modeling of deteriorating hysteretic behavior is becoming increasingly an important issue.
Several hysteretic models have been developed and can be broadly classified into two types: polygonal hysteretic model (PHM) and smooth hysteretic model (SHM). Examples of PHMs include Clough’s model (Clough 1966), Takeda’s model (Takeda et al. 1970), and the Park’s
‘‘three-parameters’’ model (Park et al. 1987). However, such models based on piecewise linear behavior have the drawback describing smooth hysteretic behavior. On the other hand, SHMs refer to models with continuous change of deteriorating behavior are more advantaged. Bouc-Wen model
(Bouc 1967; Wen 1976) and Ozdemir’s model (Ozdemir 1976) are examples of SHMs.
In this thesis, the hysteretic model proposed by Sisvaselvan and Reinhorn (2000) and modified by Chao (2005) is used. The deteriorating hysteretic behavior describing the effects of pinching, stiffness and strength degradation can be modeled by three springs (Fig2.2): the post yielding spring kkk(), hysteretic spring () and slip-lock spring ().The stiffness of the combined system is phs
kkhsk！k？k！k？ (2.1) pallpk？khs
kwhere : Instantaneous stiffness of post yielding spring; p
k: Instantaneous stiffness of hysteretic spring; h
k: Instantaneous stiffness of slip-lock spring. s
k(1) Post Yield Spring A linear spring represented the post yielding spring is written as: p
k(whereis the total initial stiffness (elastic) and is the ratio of post yielding to initial stiffness o
k(2) Hysteretic spring This purely elastoplastic spring has a smooth transition from the h
elastic to the inelastic range displaying degradation phenomena and can be described as:
mwhere: Yield moment y
？: Portion of the applied moment shared by series hysteretic spring and slip-lock spring m
: Parameter controlling the smoothness of transition from the elastic range to inelastic range N
(: Parameter controlling the shape of unloading curve; h
，，: Parameter defining stiffness and strength deterioration in a certain excursion;kl
，，The definition of, is given by: kl
?where: Yield curvature y
E: Energy dissipated in excursion i h,i
；,；: Parameters controlling the degrading velocity kl
k(3) Slip-Lock Spring Crack closure or bolt slip usually result in pinched hysteretic loop. s
Therefore, an additional spring is added in series to the hysteretic spring to model this effect. The
stiffness of slip-lock spring is written as:
，12？，??？??""??：(，，，m(1)m??，R()21??lysmaxmax：???！，kexp (2.6) ??s：?，，，，~?(1()m2?(1()m??lyly??，?????