Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, an appropriate data analysis and system identification technique is required to interpret the measured data and to identify the state of the structure. Generally, the recursive system identification algorithm is used. In this study, the recursive subspace identification (RSI) algorithm based on the matrix inversion lemma algorithm with oblique projection technique (RSI-Inversion-Oblique) is applied to investigate the time-varying dynamic characteristics. The user-defined parameters used in the RSI-Inversion-Oblique technique are carefully discussed, which include the size of the data Hankel matrix (i), model order to extract the physical modes, and forgetting factor (FF) to detect the time-varying system modal frequencies. Response data from the Northridge earthquake from the Sherman Oaks building (CSMIP) is used as an example to examine a systematic method to determine the suitable user-defined parameters in RSI. It is concluded that the number of rows in the data Hankel matrix significantly influences the identification of the time-varying fundamental modal frequency of the structure. An algorithmic model order selection method using the eigenvalue distribution of RSI-Inversion can detect the system modal frequencies at each appending data window without causing any abnormality.

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. Among these techniques tracking modal parameters and estimating the structural current state from its seismic response measurement can provide useful information for structural safety assessment, therefore, on-line or recursive identification technique needs to be developed for structural seismic response monitoring. In this paper, the recursive subspace identification algorithms based on matrix inversion lemma algorithm (RSI-Inversion) with oblique projection technique was developed. Forgetting factor with enlarge window is introduced in the RSI-Inversion to emphasize the latest state of the time-varying system in this method. In addition to identifying the instantaneous dynamic characteristics of the structural system using RSI, a two-stage damage detection algorithm incorporated with the identified results from RSI will also be applied to localize and quantify the structural damage. Seismic responses of a base-isolated bridge are used to verify the proposed identification and the damage assessment algorithms, i.e. specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. In this study, the recursive subspace identification with Bona-fide LQ renewing algorithm (RSI-BonaFide-Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios, and mode shapes at each instant of time during the strong earthquake excitation. From which the least square stiffness method (LSSM) combined with the model updating technique, called efficient model correction method (EMCM), is used to estimate the first-stage system stiffness matrix using the simplified model from the previously identified modal parameters (nominal model). In the second stage, 2 different damage assessment algorithms related to the nominal system stiffness matrix were derived. First, the model updating technique, called EMCM, is applied to correct the nominal model by the newly identified modal parameters during the strong motion. Second, the element damage index can be calculated using element damage index method (EDIM) to quantify the damage extent in each element. Verification of the proposed methods through the shaking table test data of 2 different types of structures and a building earthquake response data is demonstrated to specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.

This study presents a structural health monitoring method for damage identification and localization of a structure, which incorporated with the principal component analysis (PCA) based data compression and pattern recognition. Through the distribution of sensing node in the structure, an experimental twin-tower steel structure on shaking table test, the dynamic response at different point in the structure is collected. Two different damage scenarios are created in the structure: (1) buckling of the first story bracing member of tower A, (2) buckling of the 2nd floor bracing member of tower A. To extract the features from the vibration measurement, first, stochastic subspace identification and recursive subspace identification methods were applied to extract the modal parameters of their structural system. Then the FRF-based damage assessment using PCA data compression and the scalogram-based novelty detection are used to obtained patterns in some significant respect on damage assessment. Finally, based on the change of flexibility matrix of the system, damage location can be identified..

Tracking modal parameters and estimating the structural current state from building seismic response measurement can provide useful information for building safety assessment, therefore, on-line or recursive identification technique needs to be developed for building seismic response monitoring. In this paper, three recursive subspace identification algorithms are developed. One is the recursive subspace identification with Bona-fide LQ renewing algorithm (RSI-BonaFide), one is recursive subspace identification based on matrix inversion lemma algorithm (RSI-Inversion) either with oblique projection technique or with orthogonal projection technique. A forgetting factor is introduced in the RSI-Inversion to emphasize the latest state of the time-varying system in this method. Two different sets of building seismic response data are used to verify the applicability of the proposed methods. One is the 3-story steel structure with abrupt change of story stiffness shaking table test in laboratory, the other is the seismic response analysis of a 9-story mid-story isolation building.

Since tracking modal parameters and estimating the structural current state from building seismic response measurement can provide useful information for building safety assessment, online or recursive identification techniques need to be developed and implemented on building seismic response monitoring. In this article, two recursive subspace identification algorithms are developed. One is the recursive subspace identification with BonaFide LQ renewing algorithm (recursive subspace identification BonaFide) incorporated with moving window technique to identify modal parameters at each time instant during the earthquake excitation. Besides, recursive subspace identification based on matrix inversion lemma algorithm (recursive subspace identification Inversion) is also used and keeps the same data window with recursive subspace identification BonaFide only for the initial identification and then appends the following data points to identify modal parameters for the whole excitation time history. A forgetting factor is introduced to emphasize the latest state of system in this method. Two different sets of building seismic response data are used to verify the applicability of the proposed methods. One is the three-story steel structure with abrupt change of story stiffness shaking table test in laboratory, the other is a series of seismic response of a four-story-reinforced concrete elementary school building, including several large seismic events. It is concluded that both methods can detect the time when the floor stiffness was changed but recursive subspace identification Inversion with forgetting factor can provide more accurate estimation of the change of stiffness.

SummaryTracking modal parameters and estimating the current structural state of a building from seismic response measurements, particularly during strong earthquake excitations, can provide useful information for building safety assessment and the adaptive control of a structure. Therefore, online or recursive identification techniques need to be developed and implemented for building seismic response monitoring. This paper develops and examines different methods to track modal parameters from building seismic response data. The methods include recursive data‐driven subspace identification (RSI‐DATA) using Givens rotation algorithm, and RSI‐DATA using Bona fide algorithm. The question on how well the results of RSI‐DATA reflect the real condition is investigated and verified with a bilinear SDOF simulation study. Time‐varying modal parameters of a four‐story reinforced concrete school building are identified based on a series of earthquake excitations, including several seismic events, large and small. Discussions on the different methods' ability to track the time‐varying modal parameters are presented. The variation of the identified building modal frequencies and damping ratios from a series of event‐by‐event seismic responses, particularly before and after retrofitting of the building is also discussed. Copyright © 2017 John Wiley & Sons, Ltd.

In this study, the recursive update algorithm of subspace system identification is proposed for estimating dynamic characteristics of a time-varying multi-input multi-output (MIMO) building structure using the pastinput/ output multivariable output-error state space (PO-MOESP) based algorithm. First, the recursive subspace identification with Bona-fide LQ renewing algorithm (RSI-BonaFide-Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios and mode shapes at each time instant during the strong earthquake excitation, which assumes the equivalent linear dynamic characteristic in every moving time window with a fixed length. In addition to identifying the instantaneous dynamic characteristics of the structural system using RSI, several damage detection algorithms related to the reconstructed system stiffness matrix using simplified model was derived from the previously identified modal parameters to quantify the damage extent, specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction. To demonstrate the capability of the proposed recursive subspace identification algorithm and the damage assessment technique, dynamic response data generated from a shaking table test of a two 3-story steel structure experiment is used to verify the algorithms on detecting damage caused by nonlinear behavior occurring on the steel column. Besides, a building seismic response data (collected from Chi-Chi earthquake) was also used to evaluate the damage situation during severe earthquake excitation.

Since tracking modal parameters and estimating the structural current state from building seismic response measurement can provide useful information for building safety assessment and for the adaptive control of the structure, therefore, on-line or recursive identification techniques need to be developed and implemented on building seismic response monitoring. In this paper different methods on tracking modal parameters from building seismic response data are examined. The methods include Adjustable moving window subspace identification, Recursive 4SID-based identification algorithm with fixed input/output data size, Offl ine & recursive data-drive subspace identification with update LQ-decomposition and Recursive least square using MISO-ARX model. Based on a series of a building seismic response (a 4story RC school building), including several large seismic events, discussions on the identified time-varying modal parameters among different methods are presented. Besides, the variation of the identified building modal frequency from a series of event-by-event larg e seismic response is also discussed.