Deterministic-stochastic Subspace Identification Research Articles

Structural flexibility identification from impact test data through a subband estimation method

SummaryFlexibility is an important parameter reflecting bridge load‐carrying capacity. Dynamic testing is a fast and effective method to obtain the structural modal flexibility of small‐ and medium‐span bridges. The Deterministic‐stochastic subspace identification (DSI) algorithm is a well‐established structure identification method in the time domain. However, the estimation of damping, especially the modal scaling factor, is not always reliable due to inevitable measurement noise, which directly affects the identification accuracy of flexibility. This paper proposes a maximum likelihood estimation method in subbands (SMLE), which can be regarded as an add‐on method of the DSI algorithm because the initial parameters are obtained from the DSI algorithm. The processing of frequency band division is implemented first, and the frequency response function curve in each subband of the whole frequency range is fit separately. Then, subband cyclic iteration is proposed to improve the identification accuracy in a closely spaced mode system. The proposed SMLE method maintains the advantages of the DSI algorithm while improving the accuracy of parameter estimation and flexibility identification. Two lumped mass models are used to verify that the proposed method can effectively improve estimates to obtain a precise flexibility matrix and predict the displacement of the structure under static loading. Experimental example of a continuous girder bridge is considered to verify the availability and effectiveness of the proposed method in practice.

Cover Image

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

Performance Assessment of a High-Speed Railway Bridge through Operational Modal Analysis

Modal parameters are widely recognized as valuable indicators for evaluating the performance of railway bridges in structural health monitoring. A major challenge in the mode-based performance assessment is to obtain modal parameters reliably because operational factors may cause significant identification errors or reduce modal identifiability. To reduce the operational effects on mode-based assessment, vibration responses are divided according to excitation types, and then two subspace identification techniques are developed for identifying modal parameters of the railway bridge. If the bridge is only acted on by the ambient excitation, the stochastic subspace identification (SSI) is taken in this paper. If the bridge is mainly acted on by the train excitation, modal parameters are difficult to identify due to the regularly spaced and highly energetic axle loads. In this case, a deterministic stochastic subspace identification (DSSI) method is developed for improving the modal identifiability of the railway bridge under train action. The monitoring responses of a high-speed railway bridge are analyzed in this paper to track long-term modal parameters. Besides, variations of modal parameters that are related to environmental factors, operational conditions, modal orders, vibration directions, and member types are extensively compared. The results show that modal parameters can be well-identified even though the nonwhite noise excitation exists, and the performance assessment can be well achieved through determining the optimal modal parameters.

Time variant system identification of superstructures of base-isolated buildings

The time-variant dynamic properties related to the superstructure of base-isolated (BI) buildings are identified using a simple substructure approach. Based on the acceleration data recorded in BI buildings during earthquake events, the short-time deterministic-stochastic subspace identification (STDSI) method and a novel short-time transfer function (STTF) method are used to identify the temporal evolution of the modal properties of the superstructure, which can be consequently employed to study the evolution of its potential damage. The proposed substructure approach is applied to experimental data from three BI structures: a building numerically simulated using the commercial software SAP2000, a full-scale five-story reinforced concrete BI building tested at different intensity levels on a large-scale shake table, and an instrumented four-story reinforced masonry building located in Chile. The results indicate that the identified modal properties obtained for the superstructure by using the proposed approach are comparable to those obtained from the corresponding fixed-base (FB) buildings, allowing to study in detail the dynamic behavior of BI buildings’ superstructures disaggregating the highly inelastic response associated with the seismic isolation system.

Application of Improved Combined Deterministic-Stochastic Subspace Algorithm in Bridge Modal Parameter Identification

Modal parameter identification is considered to be one of the most important tasks in structural health monitoring because it provides a reliable reference for structural vibration control, damage severity, and operational state. Moreover, at present, the combined deterministic-stochastic subspace algorithm is cogitated as one of the key algorithms in the modal parameter identification, which is why it is widely used in the modal parameter identification of bridge structures. In this paper, a novel method is proposed, which is a time-domain identification algorithm, based on sliding window-fuzzy C-means clustering algorithm-combined with deterministic-stochastic subspace identification (SC-CDSI), to achieve online intelligent tracking and identification of modal parameters for nonlinear time-varying structures. First of all, to realize the online tracking and identification process, it is necessary to divide the input and output signal of the nonlinear time-varying structure by windowing; for that, to determine the window function, window size and window step length according to the characteristics of the signal are analyzed. Secondly, in order to satisfy the intelligent identification of effective modals in stability diagram, the fuzzy C-means clustering algorithm is kept as a base, whereas frequency, damping ratio, and modal shapes serve as clustering elements, applied to fuzzy C-means clustering algorithm, and then the intelligent selection of effective modals is achieved. Finally, a shaking table test bridge is used as a modal parameter identification in lab, and its results are compared with the MIDAS finite element results. The compared results show that the proposed SC-CDSI identification algorithm can accurately achieve the intelligent identification of online tracking of the structural frequency, and the identification results are reliable to be used in real-life bridge structures.

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.

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...

Fatigue damage identification in threaded connection of tubular structures through in-situ modal tests

The use of threaded connection is a valuable alternative to conventional welding in tubularconstructions, e.g. pipelines, drill pipes and deep water risers. Those applications are normally exposed toenvironmental hazards – wave induced vibrations, temperature changes, etc. – as well as subjected tosevere service conditions. A classical way to determine fatigue strength in many engineering situations is tocalibrate material models by means of ad hoc designed experiments. Unfortunately, it is very difficult in thiscase even under laboratory conditions due to complicated stress and strain states in the contacting taperedhelical thread surfaces of the connection. Therefore, a classical four-point bending fatigue test setup hasbeen built with a real pipe specimen of 3.75 meter long, consisting of two standard API pipes connected bya threaded coupling, under unsymmetric (non-zero average) load control cycles. A complete vibration studyhas been carried out based on input-output modal tests for the entire period of the fatigue experiment. Inputexcitation is due to hammer impact and responses are recorded by accelerometers and by reusabledynamic strain gauges. The measured modal strains from the dynamic strain gauges allow for directcalculation of the modal curvatures, rather than deriving approximately from acceleration information. Bycomparing the measured modal parameters with those of a numerical model of the same structure inundamaged condition, damage detection, localization in the coupling and quantification are possible. Thisstudy leads to the following conclusion of practical use: the recent advancement in modal analysis, i.e. thereference based input-output combined deterministic-stochastic subspace identification, makes it possibleto identify the structural modal properties from in-situ modal tests, which are performed while the fatiguetest is ongoing. In this way the fatigue test is uninterrupted to avoid the problem of stress and straindisturbances happened in un-reversing load cycles test.

A new insight to the matrices extraction in a MOESP type subspace identification algorithm

In this paper we analyse the estimates of the matrices produced by the non-biased deterministic-stochastic subspace identification algorithms (NBDSSI) proposed by Van Overschee and De Moor (1996). First, an alternate expression is derived for the A and C estimates. It is shown that the Chiuso and Picci result (Chiuso and Picci 2004) stating that the A and C estimates delivered by this algorithm robust version and by the Verhaegen's MOESP (Verhaegen and Dewilde 1992a, Verhaegen and Dewilde 1992b, Verhaegen 1993, Verhaegen 1994) are equal, can be obtained from this expression. An alternative approach for the estimation of matrices B and D in subspace identification is also described. It is shown that the least squares approach for the estimation of these matrices estimation can be just expressed as an orthogonal projection of the future outputs on a lower dimension subspace in the orthogonal complement of the column space of the extended observability matrix. Since this subspace has a dimension equal to the number of outputs, a simpler and numerically more efficient (but equally accurate) new subspace algorithm is provided.

Choice of state-space basis in combined deterministic-stochastic subspace identification

This paper describes how the state-space basis of models identified with subspace identification algorithms can be determined. It is shown that this basis is determined by the input spectrum and by user-defined input and output weightings. Through the connections between subspace identification and frequency-weighted balancing, the state-space basis of the subspace-identified models is shown to coincide with a frequency-weighted balanced basis.