Deterministic-stochastic Subspace Identification Method Research Articles

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The cover image is based on the Research Article A data-driven combined deterministic-stochastic subspace identification method for condition assessment of roof structures subjected to strong winds by Xuan Liu et al., https://doi.org/10.1002/stc.3031

Time-Variant Modal Parameters and Response Behavior of a Base-Isolated Building Tested on a Shake Table

This paper presents the identification of the instantaneous modal properties and the experimental response of a full-scale, five-story base-isolated RC building tested on a shake table. A suite of earthquake motions of various intensities was applied to the building to progressively increase the seismic demand. The deterministic-stochastic subspace identification method is employed to estimate the variations of the modal properties of the building by employing a short-time windowing approach. The changes of the modal parameters during the seismic motions are tracked and analyzed. Observed and measured responses of the structure are analyzed and correlated with the variation of the identified modal parameters. The nonlinear behavior of the isolators generates the variation of the identified natural frequencies and equivalent damping ratios of the building, which change in agreement with the input motion intensity. A high correlation between the effective stiffness of the isolators and the instantaneous frequency of the first mode is found. The effective damping ratio of the isolation system and the instantaneous damping ratio of the fundamental mode of the building are highly correlated.

Error analysis of the application of combined subspace identification to the modal analysis of railway vehicles

This study is part of the development of a methodology for the application of the combined deterministic-stochastic subspace identification method for the identification of the modal parameters of railway vehicles. The proposed methodology employs the vertical accelerations measured on the axle boxes of one wheelset as excitations and the accelerations measured in the carbody and bogies as responses, which are registered when the vehicle is in circulation. With this aim, first the parameters that may affect the modal identification accuracy are identified. Then, they are grouped into three categories: parameters associated with the vehicle, parameters related with the excitation that the vehicle receives and parameters associated with the test execution. Next, an index named Modal Parameter Error Index (MPEI) is introduced. This index allows estimating the error that will be obtained in the identification of the natural frequency and damping ratio of the modes based on the knowledge of the parameters of the test. The terms that compose the index have been obtained applying the Monte Carlo method in numerical simulations for simple models. The availability of MPEI is a very powerful tool in the application of the combined subspace identification method for identifying modal parameters of railway vehicles. Also, based on MPEI and the expected variation range of the influencing factors, useful application guidelines are given.

Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake

A model updating methodology is proposed for calibration of nonlinear finite element (FE) models simulating the behavior of real-world complex civil structures subjected to seismic excitations. In the proposed methodology, parameters of hysteretic material models assigned to elements (or substructures) of a nonlinear FE model are updated by minimizing an objective function. The objective function used in this study is the misfit between the experimentally identified time-varying modal parameters of the structure and those of the FE model at selected time instances along the response time history. The time-varying modal parameters are estimated using the deterministic–stochastic subspace identification method which is an input–output system identification approach. The performance of the proposed updating method is evaluated through numerical and experimental applications on a large-scale three-story reinforced concrete frame with masonry infills. The test structure was subjected to seismic base excitations of increasing amplitude at a large outdoor shake-table. A nonlinear FE model of the test structure has been calibrated to match the time-varying modal parameters of the test structure identified from measured data during a seismic base excitation. The accuracy of the proposed nonlinear FE model updating procedure is quantified in numerical and experimental applications using different error metrics. The calibrated models predict the exact simulated response very accurately in the numerical application, while the updated models match the measured response reasonably well in the experimental application.

Damage detection of structures identified with deterministic-stochastic models using seismic data.

A deterministic-stochastic subspace identification method is adopted and experimentally verified in this study to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV) is then considered for damage detection. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged counterpart has also been studied. This study gives further insights into the scheme in terms of effectiveness, robustness, and limitation for damage localization of frame systems.

Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems

This paper proposes the use of the deterministic-stochastic subspace identification (DSI) method, an input-output parametric linear system identification method, for characterization of nonlinear dynamic structural systems based on their time-varying amplitude-dependent instantaneous (i.e., based on short time-windows) modal parameters. Performance of the DSI method for estimation of instantaneous modal parameters of nonlinear systems is investigated using numerical as well as experimental data. In this study, DSI is used for extracting instantaneous modal parameters of single degree-of-freedom (SDOF) as well as 7-DOF systems with different hysteretic material behavior. Nonlinear responses of the SDOF and 7-DOF systems are simulated due to different seismic excitations using the OpenSees structural analysis software. Modal identification results are compared with those obtained using wavelet transform and the exact values. Effects of four input factors are studied on the variability of identified instantaneous modal parameters: (1) type of material nonlinearity, (2) level of nonlinearity, (3) input excitation, and (4) length of data windows used in the identification. The accuracy of the identified instantaneous modal parameters is evaluated along the response time history while varying the above mentioned input factors. Overall, DSI outperforms the wavelet transform for short-time/instantaneous modal identification of nonlinear structural systems and provides reasonably accurate results especially when the material hysteretic behavior is smooth such as the considered Giuffré-Menegotto-Pinto hysteretic model. Finally, DSI has been applied for short-time modal identification of a full-scale seven-story reinforced concrete shear wall structure based on its measured response to different seismic base excitations on a shake table. The identified instantaneous natural frequencies of the first vibration mode can accurately track the variation in the structure's effective stiffness along its response.

Finite-Element Model Updating for Assessment of Progressive Damage in a 3-Story Infilled RC Frame

AbstractThis paper presents a study on the identification of progressive damage, using an equivalent linear finite-element model updating strategy, in a masonry infilled RC frame that was tested on a shake table. A two-thirds-scale, 3-story, 2-bay, infilled RC frame was tested on the UCSD–NEES shake table to investigate the seismic performance of this type of construction. The shake table tests induced damage in the structure progressively through scaled historical earthquake records of increasing intensity. Between the earthquake tests and at various levels of damage, low-amplitude white-noise base excitations were applied to the infilled RC frame. In this study, the effective modal parameters of the damaged structure have been identified from the white-noise test data with the assumption that it responded in a quasi-linear manner. Modal identification has been performed using a deterministic-stochastic subspace identification method based on the measured input–output data. A sensitivity-based finite-ele...