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Most ground-motion models (GMMs) parameterize the earthquake source by magnitude, style of faulting, and source depth. GMMs are isotropic in terms of the source scaling for these three parameters. The radiation pattern, which leads to azimuthally varying source effects, is not included in most GMMs. As a result, any systematic radiation-pattern effects are treated as aleatory variability in the path terms in the GMMs, which does not make physical sense. We incorporate the far-field radiation pattern into GMMs for pseudospectral acceleration and Fourier amplitude spectra for the Taiwan region. A key issue is how to combine the radiation pattern from the SH and SV components for predicting the RotD50 amplitudes of ground motions used in GMMs. A suite of point-source simulations was generated for a range of focal mechanisms and site azimuths. Empirical models for the phase differences between the radial and transverse components were developed to constrain the between-component phase differences in simulations. The results show that the vector sum of the SH and SV far-field radiation patterns, FS, has a higher correlation with the RotD50 amplitudes of the ground motion than the arithmetic mean or the geometric mean. The radiation-pattern term is modeled by S0(M)+S1(M)ln(Fs+S2), in which S0(M) and S1(M) are linear functions of magnitude between M 4 and 6; they equal 0 for M > 6. The magnitude dependence reflects that, for large magnitudes and short distances, ground motions are more affected by the slip distribution and rupture timing than by the average radiation pattern from the subevents along the rupture, but the radiation pattern has a significant effect on the long-period ground-motion amplitude for small-magnitude events. Including radiation patterns into GMMs will improve estimates of 3D path effects from small-magnitude events by removing radiation-pattern effects from combined radiation-pattern and path terms used in current GMMs.

We propose a methodology to implement horizontal-to-vertical Fourier spectral ratios (HVRs) evaluated from strong ground motion induced by earthquake (EHVRs) or ambient ground motion observed from microtremor (MHVRs) individually and simultaneously with the spatial correlation (SC) in a ground-motion prediction equation (GMPE) to improve the prediction accuracy of site effects. We illustrated the methodology by developing an EHVRs-SC-based model which supplements Vs30 and Z1.0 with the SC and EHVRs collected at strong motion stations, and a MHVRs-SC-based model that supplements Vs30 and Z1.0 with the SC and MHVRs observed from microtremors at sites which were collocated with strong motion stations. The standard deviation of the station-specific residuals can be reduced by up to 90% when the proposed models are used to predict site effects. In the proposed models, the spatial distribution of the predicted station terms for peak ground acceleration (PGA) from MHVRs at 3699 sites is consistent with that of the predicted station terms for PGA from EHVRs at 721 strong motion stations. Prediction accuracy for stations with inferred Vs30 is similar to that of stations with measured Vs30 with the proposed models. This study provides a methodology to simultaneously implement SC and EHVRs, or SC and MHVRs in a GMPE to improve the prediction accuracy of site effects for a target site with available EHVRs or MHVRs information.

We develop a ground motion prediction equation (GMPE) for estimating horizontal ground motion amplitudes caused by crustal earthquakes, based on an integrated data set that includes strong motion recordings mainly from Taiwan earthquakes and only from large magnitude earthquakes in the NGA-West2 database. This GMPE is developed for probabilistic seismic hazard analysis study, which is introduced as a part of Taiwan Senior Seismic Hazard Analysis Committee Level 3 projects. The functional form developed by Chiou and Youngs was carefully studied to determine the key modeling parameters needed to regress against ground motion in the target region. Using this functional form, the GMPE achieves considerable improvement over previously developed Taiwan GMPEs. In particular, the use of a high-order function in magnitude scaling enables representation of the saturation effects of large earthquakes. Moreover, consideration of focal mechanisms, depth effects, and dip effects are used to correct the magnitude scaling; consideration of nonlinear site amplification is conditioned on VS30and reference ground motion on rock; and consideration of basin depth effect is a function of Z1.0in correlation with VS30. In addition, ground motion data used in this study are not only expanded by more than three times as many earthquakes and records compared with a previous Taiwan model but also provide the metadata of these records that were not available or were previously incomplete. In this study, we compare the proposed model with the NGA-West2 models and discuss the regional difference in ground motion in terms of spectral shape, magnitude scaling, distance scaling, depth scaling, style of faulting, and site effects. We provide median and single standard deviations of peak ground acceleration and 5% damped pseudospectral acceleration response ordinates of the orientation-independent average horizontal component of ground motion (RotD50) for the spectral period of 0.01–10 s.

An earthquake with an epicenter offshore of Hualien City in eastern Taiwan occurred at midnight on February 6, 2018. The Richter magnitude (ML) of the earthquake was 6.26 and the seismic intensity ranged up to level VII, the strongest seismic intensity level regulated in Taiwan. Almost all the major damage resulting from this seismic event was occurred near both sides of the Milun Fault, where records from nearby strong motion stations displayed the characteristics of near-fault ground motions. The main seismic damage was the collapse of four buildings with soft bottom stories, one of which resulted in fourteen of the seventeen total fatalities. Comparing the acceleration response spectra with the design response spectra sheds light on the effects of near-fault ground motions on the collapsed buildings. Based on the eventual forms of collapsed buildings, building collapses that have generally led to major casualties in past seismic events around the world can be classified into sit-down, knee-down and lie-down types. In addition to the four collapsed buildings, seismic reconnaissance on other buildings, bridges, ports, and non-structural components have also been conducted. This study explores the issues and challenges arising from the reconnaissance results and thereby enhances learning from the seismic event.

A shaking table test of a three-story reinforced concrete (RC) building was conducted. The tested building is vertically irregular because of the first story’s elevated height and the third story’s added RC walls. In addition to far-field ground motions, near-fault ground motions were exerted on this building. A numerical model of the three-story building was constructed. Comparing with the test results indicates that the numerical model is satisfactory for simulating the seismic response of the three-story building. This validated numerical model was then further applied to look into two issues: the effective section rigidities of RC members and the effects of near-fault ground motions. The study results show the magnitude of the possible discrepancy between the actual seismic response and the estimated seismic response, when the effective section rigidities of the RC members are treated as in common practice. An incremental dynamic analysis of the three-story RC building subjected to one far-field and one near-fault ground motion, denoted as CHY047 and TCU052, respectively, was conducted. In comparison with the far-field ground motion, the near-fault ground motion is more destructive to this building. In addition, the effect of the selected near-fault ground motion (i.e. TCU052) on the building’s collapse is clearly identified.

In this study, a new horizontal ground-motion model is developed for crustal and subduction earthquakes in Taiwan. A novel two-step maximum-likelihood method is used as a regression tool to develop this model. This method simultaneously considers both the correlation between records and the biased sampling because of random truncation. Moreover, additional ground-motion data can be considered to derive more reliable analysis results. The functional form of the proposed ground-motion model is constructed using the response spectrum of the reference ground-motion scenario and different scalings of the source, path, and site to illustrate the ground-motion characteristics. The variabilities in the ground-motion intensity that result from different events, stations, and records are developed individually to derive a single-station sigma. The proposed ground-motion model may be useful for predicting ground-motion intensity and performing site-specific probabilistic seismic hazard analysis in Taiwan.

A ground motion prediction equation (GMPE) is presented for computing the median and standard deviation of peak ground acceleration (PGA) and 5% damped pseudo-spectral acceleration (PSA) for periods between 0.01 s and 5.0 s for probabilistic seismic hazard analysis (PSHA) and engineering applications in Taiwan. An integrated strong motion dataset consisting of two subduction earthquake regions was selected from 3314 recordings from Taiwan with M4.5 to M7.1 and 3376 recordings from Japan with M6.5 to M9.1. This dataset was then used to validate, and refit where necessary, the function form provided by Abrahamson et al. for application to Taiwan subduction earthquakes. The proposed model accounts for the extrapolation behaviors associated with the large-magnitude scaling and the near-source scaling terms, both of which were developed empirically by using the combined Taiwan–Japan dataset. The distance attenuation and site term were developed specifically for the Taiwan region. The site term is based on two parameters; the time-averaged shear wave velocity of the top 30 m depth ( VS30) and the depth-to-the-shear wave velocity horizon of 1.0 km/s ( Z1.0).

Regression analysis is a basic and essential tool for developing the ground motion prediction equation (GMPE). Generally, the probability of intensity measurement for a given ground motion scenario described by several predictors is assumed to be normally distributed. However, because of the triggering threshold of the strong-motion station, ground motion records below the triggering threshold are truncated (i.e., not recorded), and the truncated intensity levels of spectral accelerations at different periods are random variables. Consequently, the sampling of the ground motion data used in GMPE development is biased, and the observed probability of the intensity measurement is no longer normally distributed. Therefore, a novel two-step maximum-likelihood method is proposed in this paper as a regression tool to overcome this problem in GMPE development. The advantage of the proposed method is that the correlation between records from the same events and those from the same sites as well as the biased sampling problem can be considered simultaneously, and more ground motion data can be considered to derive more reliable analysis results.

Site amplification behavior are important in ground motion prediction. Seismic waves were amplified and caused significant building damages in the Taipei Basin by the 1986 Hualien offshore (subduction interface) and the 1999 Chi-Chi earthquakes (crustal), for which both of the epicentral distances were nearly 100 km. To understand local site amplifications in Taiwan, empirical site amplification factors for both horizontal and vertical ground motions are studied using recently constructed strong motion and site databases for the free-field TSMIP stations. Records of large magnitude earthquakes of MW larger than 5.5 from 1991 to 2016 were selected for this study. Site amplification factors at site conditions with Vs30 between 120 m/s to 1600 m/s and bedrock accelerations up to 0.8 g were evaluated using ratios of spectral accelerations at different periods. The reference site condition, i.e. the engineering bedrock, is assumed as Vs30 of 760 m/s (B/C boundary) in this study. Our empirical site amplification form are borrowed from the site response function of ASK14 and CY14 ground motion models in NGA-West2 project with slight modification. Therefore our site amplification model includes a linear amplification term and a nonlinear deamplification term. The coefficients of the empirical models were obtained by a nonlinear regression analysis using the selected Taiwan data. Site amplification factor is a function of Vs30 and spectral intensity in the model. Similar linear site amplification factor to the NGA models is derived in our model; however, more significant soil nonlinearity behavior than the NGA models is likely captured from the empirical data. The amplification factor in vertical component is smaller than that in horizontal.

Supplemental material, Electronic_Supplement_3_-_Summary_of_Function_Form for A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan by Shu-Hsien Chao, Brian Chiou, Chiao-Chu Hsu and Po-Shen Lin in Earthquake Spectra

Supplemental material, Electronic_Supplement_4_-_List_of_Selected_Events for A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan by Shu-Hsien Chao, Brian Chiou, Chiao-Chu Hsu and Po-Shen Lin in Earthquake Spectra

Supplemental material, Electronic_Supplement_5_-_Comaprison_of_the_Taiwan_Ground_Motion_Models for A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan by Shu-Hsien Chao, Brian Chiou, Chiao-Chu Hsu and Po-Shen Lin in Earthquake Spectra

In probabilistic seismic hazard analysis (PSHA), the standard practice is to select a set of appropriate ground motion prediction equations (GMPEs) and assign weights on the logic tree, especially for regions where strong motion data are sparse and where no indigenous GMPE exists. Subjectively assigning weights to a set of models usually has the disadvantage of not obtaining mutually exclusive and collectively exhaustive models because of sparse or unavailable data. Therefore, the development of logic tree weightings in PSHA remains a major challenge. In this study, a distance metric measure for GMPEs is first analyzed to show how a set of GMPE’s prediction models can be partially reconciled by using high-dimensional information visualization techniques. Visualization of a large suite of GMPEs onto a 2-D graphical map provides a powerful theoretical framework that can guide the selection of a set of representative models. These models are considered mutually exclusive and collectively exhaustive, and have the ability to represent the center, body, and range of ground-motion distribution in a logic tree analysis. Second, determination a set of weights for PSHA are estimated based on the residuals, likelihood and EDR-index which are known as data – driven weight. The other weight type is non-data driven which is calculated based on the probability of a random model generated on a Sammon’s map. The methods presented here, that improve consistency in the weight assignment, can help to reduce overall epistemic uncertainties and offer a way of assigning weight on the logic tree. Finally, an example for assigning the weights on the logic tree for PHSA are discussed.

A 7-story reinforced concrete building with a soft bottom story and plan-asymmetry in one horizontal direction was collapsed on a shake table by generation of bi-directional near-fault ground motions. The numerical model of the 7-story building is introduced and verified through a comparison with the experimental results. The hysteretic models of the verified numerical model are calibrated according to static cyclic component tests. To assume the condition that the static cyclic component tests are not available, the hysteretic models of some critical structural components are intentionally altered. Three additional numerical models of the building, which serve as the distorted numerical models, are obtained from the combinations of the altered hysteretic models. Incremental dynamic analyses (IDA) are applied to the four numerical models of the building (i.e., one verified model and three distorted models). Comparing the IDA results of the four numerical models helps to elucidate the effect of the hysteretic models on the full range of the seismic responses (i.e., from elastic response to total collapse) of the building.

Summary This paper addresses the issue of structural system identification using earthquake-induced structural response. The proposed methodology is based on the subspace identification algorithm to perform identification of structural dynamic characteristics using input–output seismic response data. Incorporated with subspace identification algorithm, a scheme to remove spurious modes is also used to identify real system poles. The efficiency of the proposed method is shown by the analysis of all measurement data from all measurement directly. The recorded seismic response data of three structures (one 7-story RC building, one midisolation building, and one isolated bridge), under Taiwan Strong Motion Instrumentation Program, are analyzed during the past 15 years. The results present the variation of the identified fundamental modal frequencies and damping ratios from all the recorded seismic events that these three structures had encountered during their service life. Seismic assessment of the structures from the identified system dynamic characteristics during the period of their service is discussed. Copyright © 2014 John Wiley & Sons, Ltd.

The objective of this paper is to discuss two different categories on structural damage detection: One is the centralized feature extraction technique by using multi-sensor architecture and the other is the pattern-level data fusion by using the extracted features from individual sensor. The covariance-driven stochastic subspace identification and multivariate singular spectrum analysis are applied for the centralized feature extraction. For pattern-level feature recognition wavelet packet transforms and power spectral density from individual sensing record is used. Through both centralized and pattern-level feature extraction the results can not only detect the occurrence of structural damage but also can locate the damage. Finally, the dynamic finite element model updating is used for damage quantification. Verification of the proposed algorithms by using a research-scale bridge scouring test model to detect the damage occurrence and severity during scouring is presented. Finally, discussion on the computation effectiveness among different method is made.

To detect and locate the structural damage from direct measurements can be done only when the sensors are very closely located to the damage initiating point, which is generally impossible to predict, particularly for the reinforced concrete structures. With the availability of high-resolution distributed sensing, using optical tracker on light targets, the damage location as well as the level of damage can be identified. The objective of this article is to conduct structural system identification of a reinforced concrete frame by using the proposed structural integrity index (identify the element curvature and null-space damage index) and the estimation of finite element strain. Finally, a discussion on the identified time-varying system natural frequency and stiffness/strength degradation of the reinforced concrete structure from global measurement in relation to the calculated structural integrity index using optical sensing array data and element strain on the identification of damage location and damage severity are presented.

In this article, a systematic way of structural damage assessment algorithm, including identification of damage location and damage quantification, is proposed using output-only measurement. First, the null-space-based and subspace-based damage detection methods are used to confirm the damage severity of a structure. Then, the stochastic subspace identification technique is adopted to identify the time-varying system natural frequencies from the global response measurement. Finally, the novelty index, defined as the Euclidean norm of the time–frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structures, is applied to locate the damage. To quantify the damage, the complete system realization is obtained from the identified modal properties through stochastic subspace identification method. From which, the inter-story stiffness reduction ratio can be identified using the normalized stiffness matrix. For case of limited measurement, the multi-setup operational modal analysis is applied to construct the complete system matrix. Verification of the proposed damage assessment algorithm using response data from a series of shaking table test of a six-story steel structure with the cut in column member to simulate the damage is demonstrated.

Singular spectrum analysis (SSA) is a novel technique and has proven to be a powerful tool for time series data analysis. Through singular value decomposition of Hankel matrix data, the time series of data can be decomposed into several simple, independent and identifiable components from singular values and singular vectors. It has already been widely applied to process climatic, meteorological, geophysical and economic data. In this paper, we demonstrate that the coupling degree of the 1st and 2nd singular values in SSA contains useful indications on the feature and composition of the analysed signal. The proposed method is successfully applied to the monitoring of structure, such as damage detection of the simulated dynamic system, experimental steel frame, bridge foundation scouring and pier settlement in the laboratory and on-site bridge monitoring during typhoon strike. The proposed algorithm is simple and suitable for structural health monitoring in the field.

Reinforced concrete structure may exhibit significant inelastic hysteretic behavior when subject to strong earthquake excitation. To investigate such an inelastic behavior, in this study, a new system identification technique is applied by using the deteriorating distributed element (DDE) model to simulate the hysteretic behavior of a degrading structure. Through the advanced signal processing technique, the multiple singular spectrum analysis (SSA) and the nonlinear SSA, the recorded inelastic restoring force of a deteriorating structure can be decomposed into several independent additive components in its sequentially degrading order and with decreasing weight. With each decomposed hysteresis loop, the model parameters of the DDE model are identified. The evolutionary properties of the progressive stiffness degradation behavior of reinforced concrete structure can be observed from the identified model parameters. Finally, comparison on the physical properties of the identified DDE model with respect to the seismic response data of the deteriorating structure is also discussed. The result shows that the proposed identification technique can have a good estimation on the seismic behavior of the degrading structure. Copyright © 2012 John Wiley & Sons, Ltd.

From the point of view of structural safety monitoring, the state of damage after severe loading becomes an important issue for safety evaluation. In this study, seismic response data of a total of four reinforced concrete frames, designed with same dimensions and same seismic design code, subject to different levels of ground excitation individually from shaking table test, are used to study the nonlinear and damage pattern of reinforced concrete structure. First, the signal-based damage identification method, which include the change of the Hilbert marginal spectrum, the instantaneous frequency and phase difference, the Holder exponent, and the wavelet component energy distribution, is applied to identify the nonlinear features of the structure. Then the general Bouc–Wen hysteretic model was used to identify the physical parameters such as stiffness degradation, strength deterioration and hysteresis behavior of the reinforced concrete frame. Finally, the relationship between the change of model properties, the global damage index and the identified damage features are investigated. The relationship between the identified stiffness degradation function and the identified structural nonlinear/damage features can be used as a safety assessment index for the seismic assessment of reinforced concrete structure. Copyright © 2010 John Wiley & Sons, Ltd.

A biaxial hysteretic model is developed to take into account the commonly observed hysteretic characteristics of strength and stiffness degradation, pinching and biaxial interaction. The concept of zero force point is proposed to develop the biaxial hysteretic model. Two non-linear inelastic springs and one linear elastic spring are connected in parallel to define the cyclic behavior of the proposed biaxial hysteretic model. The proposed biaxial hysteretic model is rate-independent and capable of simulating not only global (such as story shear force versus story drift response of the whole structure) but also the local hysteretic behavior of structural member (such as moment versus curvature or plastic rotation response of a structural element). The biaxial cyclic loading test data of six reinforced concrete columns, which are designed for flexural failure and shear failure, are used to validate the proposed biaxial hysteretic model.

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi-linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P-Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non-ductile RC bridge column, a two-storey RC frame, and dynamic collapse test data of a non-ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.

Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal parameters are estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring.

Detect and locate the structural damage from direct measurements can be done only when the sensors are very closely located to the damage initiating point, which is generally impossible to predict, particularly for the reinforced concrete structures. With the availability of high resolution distributed sensing, using optical tracker on light targets, the damage location as well as the level of damage can be identified. The objective of this paper is to conduct structural system identification of reinforced concrete frame by using the proposed structural integrity index (identify element curvature and null-space damage index) and the estimation of finite element strain. Finally, discussion on the identified time-varying system natural frequency and stiffness/strength degradation of the reinforced concrete structure from global measurement in relating to the calculated structural integrity index using optical sensing array data and element strain on the identification of damage location and damage severity are presented.

Singular Spectrum Analysis (SSA) is a novel technique and has proven to be a powerful tool for time data series analysis. It takes singular value decomposition (SVD) of Hankel matrix embedded by analyzed time data series and decomposes the data into several simple, independent and identifiable components. In this paper, first, the coupling degree of the 1st and 2nd singular values through the composition of the analyzed signal in SSA is used as two important values to detect damage. Besides, based on the extracted sub-space or null-space from SVD of analytic matrix, damage detection algorithm is developed by considering the orthonormality between the sub-space and null-space. The proposed algorithms are verified using non-stationary response data of a model bridge (data from scouring test of a bridge) and field experiment of a bridge during abnormal weather condition. Discussion on the proposed methods with different assessment method to identify the occurrence of damage using SSI-DATA and SSI-COV to identified the system dynamic characteristics are also made.Copyright © 2012 by ASME

In this paer the application of output-only system identification technique, known as Stochastic Subspace Identification (SSI) algorithms, for civil infrastructures is carried out. The ability of covariance driven stochastic subspace identification (SSI-COV) was proved through the analysis of the ambient data of an arch bridge under operational condition. A newly developed signal processing technique, Singular Spectrum analysis (SSA), capable to smooth noisy signals, is adopted for pre-processing the recorded data before the SSI. The conjunction of SSA and SSICOV provides a useful criterion for the system order determination. With the aim of estimating accurate modal parameters of the structure in off-line analysis, a stabilization diagram is constructed by plotting the identified poles of the system with increasing the size of data Hankel matrix. Identification task of a real structure, Guandu Bridge, is carried out to identify the system natural frequencies and mode shapes. The uncertainty of the identified model parameters from output-only measurement of the bridge under operation condition, such as temperature and traffic loading conditions, is discussed.

Singular value decomposition (SVD) is a powerful linear algebra tool. It is widely used in many different signal processing methods, such principal component analysis (PCA), singular spectrum analysis (SSA), frequency domain decomposition (FDD), subspace identification and stochastic subspace identification method ( SI and SSI ). In each case, the data is arranged appropriately in matrix form and SVD is used to extract the feature of the data set. In this study three different algorithms on signal processing and system identification are proposed: SSA, SSI-COV and SSI-DATA. Based on the extracted subspace and null-space from SVD of data matrix, damage detection algorithms can be developed. The proposed algorithm is used to process the shaking table test data of the 6-story steel frame. Features contained in the vibration data are extracted by the proposed method. Damage detection can then be investigated from the test data of the frame structure through subspace-based and nullspace-based damage indices.

The objective of this study is the application of finite-element based damage detection techniques to identify the damage severity of reinforced concrete structures subject to different intensity level of earthquake excitation. The damage detection procedure consists of two parts: (1) identify the system dynamic characteristics using the system identification technique (subspace identification, SI) from direct input/output measurements, (2) develop damage assessment of structural members (joints) based on the progressive finite element model and large-scale optimization with nonlinear least-square technique. To verify the proposed method, first, four specimens of two-bay one-story reinforced concrete frame and one two-story reinforced frame structure, with the same design detail and same construction material properties, are tested on the shaking table with different intensity level of earthquake excitations. Integrate the Subspace Identification method and the Finite-element based model updating, damage identification of the structures are investigated. The proposed finite-element based damage identification method were found to be a very effective method for damage assessment of frame structure.

This paper presents a damage assessment method using the measurement data of restoring force from a sub-structural system. A normalized hysteretic energy (NHE ) for bi-linear model is developed as a function structural period and system ductility, which serves as a reference-based model for damage assessment. The stiffness degradation, strength deterioration and pinching effect in the inelastic hysteretic model are then determined from a series of nonlinear time history analysis of an inelastic SDOF system. Next, modification factors on the NHE for sensitivities of the inelastic model parameters are developed. Based on the identified model parameters by measuring the inelastic hysteretic behavior of the restoring force incorporated with the reference-based NHE model and the modification factor, the percentage of structural damage in relating to strength and stiffness degradation can be evaluated. Verification of the proposed method by simulation and experimental data of the cyclic loading and shaking table tests of the RC frame are conducted. Keywords: Inelastic hysteretic model, strength degradation, sti ffness degradation, pinching effect, statistical analysis