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??，?????
？，""where and: Maximum inelastic curvatures reached on the positive and negative sides ??maxmax
Rrespectively; ?: Parameters controlling the pinching characteristics of the hysteretic ：s
As a summary, the proposed inelastic model contains a total of eight parameters ;；(,N,，,；,；,R,?,： which control the behavior of hysteretic model； kls
(: Ratio of post yielding to initial stiffness ratio
: Parameter controlling the smoothness of the transition from the elastic range to the inelastic N
(: Parameter controlling the shape of the unloading curve h
；；, : Parameters controlling the degradation velocity kl
R?, and : Parameters controlling the pinching effect of the hysteretic behavior ：s
Under cyclic loading test, it found that as , the hysteretic model reduces to a bilinear N(?
(system, and with the reduction of -value, the double curvature phenomenon will be observed in h
the force-displacement of unloading curve. As for the parameters controlling the stiffness and
；；strength degradation, small value of and indicate substantial degradation whereas large kl
；；value of and no deterioration are observed. Finally, the long sliding length and less kl
R?residual deformation will produced if larger value of is assigned. Smaller values of and ：s
are related to insignificant effects on pinching phenomenon.
Indices of Seismic Demands
A statistical study will be carried out on the reduction factor, normalized hysteretic energy (NHE) and gama spectrum, where the NHE is related to the structural damage. Since that this qualitative measure includes cumulative effects of repeated cycles of inelastic response, then it is usually associated with structural damage. This index will be further used for damage diagnosis
(1) Damage index proposed by Park and Ang (1985).
A linear combination to maximum deformation response and hysteretic energy dissipation is given by:
uwhere : Ultimate monotonically displacement umon
umax: Displacement ductility ；！uy
；: Ultimate monotonically ductility umon
: A constant depends on structural characteristic and history of inelastic response. b
(2) Modified Park-Ang Damage Index
damage indices proposed by Bozorgnia and Bertero (2001 a,b) are introduced as Two revised
uelasticwhere: Maximum elastic portion deformation/uy ！；euy
；！1；！； For inelastic behavior and if response remains elastic (；?1) ee
HE: The hysteretic energy capacity under monotonically increasing lateral deformation Humon
(,(: Constants depend on the stability of hysteretic behavior 12
Three damage indices mentioned above will all be utilized in this study when the damage
diagnosis methodology is carried out.
A reference-based model for reduction factor, normalized hysteretic energy (NHE) and gama
spectrum incorporated with the proposed inelastic hysteretic system is proposed, and take NHE for
example, it can be defined as a function of inelastic hysteretic model parameters:
Nand(due to the less sensitivity of parameters on the shape of restoring force diagram, the h
functional form will only consider five parameters of the inelastic hysteretic model. The functional form can be reduced to:
Since the inelastic response of structural system during earthquake excitation is not focus on bi-linear hysteretic behavior, then the difference between the true inelastic response of the structural system and the general bilinear hysteretic response need to be investigated. As discuss before there
；；are several model parameters which control the hysteretic behavior of the system, such as , , kl
R(Parameters controlling the degradation velocity) and , (Parameters controlling the pinching s
effect of the hysteretic behavior), so the variation of model parameters to the NHE needs to be studied. In this study it is assumed that the effect of each inelastic model parameter to the response index is independent to each other. Therefore a generalized statistical based model for NHE can be assumed and expressed as:
NHE(T,)；Where is the reference-based hysteretic energy as discussed in the previous section. ref
To compensate the difference on the envelop of the inelastic hysteretic system between the reference model and the measured hysteretic response (restoring force diagram), a calibration factor
Cneeds to be implemented, . Since the yield force F and the yield displacement u are yypost，yielding
normalized between the model and the measured response, therefore only the post-yielding stiffness
(ratio -value will have to be considered to generate the calibration factor. As mentioned before the effect of post yielding will cause no damage to the structure. The characteristic parameter of
( which accounts for the second slope of restoring force diagram is first post-yielding stiffness
considered. Through a number of nonlinear dynamic analysis the effect of post-yielding stiffness ( on normalized hysteretic energy (NHE) is investigated as function of system natural period and
Cductility ratios. From this analysis the functional form of calibration factor can be cal，postyielding
obtained using two-stage regression analysis.
To develop the modification factor of stiffness degradation, strength deterioration and pinching effect between the reference-based model and the measured data, sensitivity studies are
CCCalso carried out to establish the modification factors (i.e. , and , stiffnessstrengthpinching
respectively). Sixteen earthquake ground motions are selected from the site condition of soil type-1 and are used as input excitations. Non-linear dynamic analysis of a SDOF system with the consideration of different ductility ratio and structural period is conducted. Sensitivity study on each model parameter is examined from the dynamic analysis to establish the effect of model parameter on the normalized hysteretic energy. Two stage regression analyses are carried out to establish the model equation. In the first stage, the function for NHE versus the natural period of the SDOF is
developed for each discrete value of ductility ratio. Then the effect of the ductility ratio is evaluated at the second stage.
Finally, the embedded statistical model is determined as function of not only system natural period, ductility ratios, but also the model parameters controlling different hysteretic behaviors.
C；The modification factor is to consider the effect of parameter (stiffness degradation) stiffnessk
C；and the modification factor is to consider the effect of parameter (strength degradation) stiffnessl
CR?and the modification factor is to consider the effect of parameters ,, on index ：pinchings
NHE with respect to reference-based model,
Verification on Damage Diagnosis Methodology
Five verification examples including numerical simulation and experiments are carried out on damage diagnosis to examine the proposed methodology. Numerical simulation with different excitation levels on a six-floor RC building is carried out in the first place. The results show the building deteriorated or damaged with increasing excitation levels. Other four experiments are carried to ensure the suitability of proposed method. First is a portal frame in the collapse test which indicated the severe damage during the experimental testing. Second is a RCS structure using pseudo dynamic data which shows the permanent displacement in each floor. Third is a two-story frame with different types of infill walls resulting in different types of failure. Last is column elements designed according to the 1982 version of Taiwan design code with lap splice and shear
failure. The method can successfully identify the degree of damage which can be interpreted not only on the damage index but also the contribution of each hysteretic behavior on damage index.
In this study, the embedded statistical model is established. Two different statistical models are developed: One is the development of the reference based model and the other is the modification factors with respect to the model parameters which control the hysteretic behavior with respect to the reference based model. A generalized bilinear model is selected as the reference based model. From a series of seismic response time history analysis of a SDOF system with the referenced-based inelastic model subjected to several input ground motions, the reduction factor,
and is established as a functional form of structural natural period and system ductility NHE；
ratios. Then, by taking the variation of model parameter of the inelastic hysteretic model, such as the effect of the post-yielding, stiffness, strength and pinching degradation, the seismic demand are
CCCinvestigated. One calibration factor and three modification factors ,, and postyieldingstiffnessstrength
C are established which incorporated with the reference based model as functional forms to pinching
predict the NHE and γ-spectrum.
Finally, the embedded statistical model was used for damage diagnosis both numerically NHE
and experimentally using RC frame structures. Based on the measurement of floor structural responses, particularly the structural component restoring force diagram of floor system, the model parameters of the inelastic hysteretic model are identified first. The damage diagnosis was carried out for a six floor RC building. Besides, four experimental tests was also verified including a collapse test of a non ductile RC portal frame, three story RCS frame, even cyclic loading test on two story with different types of infill walls and RC columns modeling the lap splice and shear failure. These four verifications were all provide a degree of damage using damage indices and sophisticatedly indicate the percentage of stiffness and strength degradation.