Output-only System Identification Methods Research Articles

System identification of Karun IV Dam using balanced stochastic subspace algorithm considering the uncertainty of results

Uncertainty in modal characteristics due to output-only system identification methods has been a challenge in operational modal analysis. The present study aims to extract modal parameters of Karun IV Dam (the highest arch dam in Iran) using the balanced stochastic subspace identification (B-SSI) and investigate the influence of user-defined parameters (i.e., columns and block rows of Hankel Matrix) on the uncertainty of the results. The effects of noise caused by numerical instabilities were first filtered using the inverse process by the condition number. Subsequently, the modal properties were homogenized with spatial clustering of applications with noise (DBSCAN) to remove the outlier and spurious characteristics. Then, the physical modes were validated by inspecting the complexity of the mode shapes based on the mode complexity factor criterion. Finally, the coefficient of variation (CV) of the validated clusters was employed to conduct a sensitivity analysis performed concerning the dimensions of the Hankel matrix to find the optimal models (with the minimum error in estimating the modal characteristics). The results indicated that the proposed method prevented the emergence of computational and noisy modes by regulating the extracted models, such that the first model of the structure was extracted with an error of less than 10% compared to the numerical model.

Experimental Modal Analysis of Angle Signals Based on the Stochastic Subspace Identification Method

This paper aims to verify the extraction of modal parameters from angle signals using the stochastic subspace identification (SSI) method. The use of angle signal-based mode shapes can reduce the loss of node information and enhance the robustness in curva-ture-based damage detection. In this regard, the system identification of angle signals should be first conducted prior to the damage detection. For large structures, an out-put-only system identification method should be considered for the modal analysis of an-gle signals, because artificial shaking excitation or impact excitation is practically impos-sible. In order to achieve this, the SSI method is used; it is one of the most powerful tools among the output-only system identification methods because it does not cover nonlinear problems. In order to demonstrate the system identification process of angle signals using the SSI method, the transformation matrix is assumed to represent the relationship be-tween the angular displacement and the normal displacement. Next, the modified block Hankel matrix that consists of angle signals, which can be expressed as a multiplication between the transformation matrix and displacement series vector, is constructed. The observability matrix can be estimated using the singular value decomposition for the pro-jection of the future part onto the past part of the modified block Hankel matrix. Finally, the natural frequencies and angle signal-based mode shapes are calculated using the state and observation matrices. In order to verify the results of the analytical studies, the modal properties estimated from the numerical simulation and the SSI method using angu-lar-velocity measurements are compared.

Damage identification of a reinforced concrete frame at increasing damage levels by sensitivity-based finite element model updating

This paper presents the damage identification results of an experimentally tested half-scale reinforced concrete portal frame using the sensitivity-based finite element model updating method. Progressively increasing story drifts are imposed on the frame by a displacement-controlled hydraulic actuator using single-cycle quasi-static lateral loading along the frame’s in-plane direction. System identification is performed using an output-only system identification method at different damage levels. Dynamic tests used for system identification are conducted using an electro-dynamic shaker. The objective function used for damage identification is constructed by the difference between the experimentally identified and numerically predicted modal parameters. Damage identification is performed in two steps: (1) The initial numerical model is updated to obtain a reference model using the modal parameters corresponding to the undamaged frame and (2) the reference model is updated for increasing damage levels using the modal parameters corresponding to these levels to identify existence of damage, its location and extent. The condition of the optimization problem is improved by reducing the number of design parameters. Damage identification results are presented in terms of stiffness reduction factors assigned to the column(s) bottom and beam ends and they correlate very well with the visual damage inspections done during the quasi-static tests.

Estimation of hysteretic damping of structures by stochastic subspace identification

Output-only system identification techniques can estimate modal parameters of structures represented by linear time-invariant systems. However, the extension of the techniques to structures exhibiting non-linear behavior has not received much attention. This paper presents an output-only system identification method suitable for random response of dynamic systems with hysteretic damping. The method applies the concept of Stochastic Subspace Identification (SSI) to estimate the model parameters of a dynamic system with hysteretic damping. The restoring force is represented by the Bouc-Wen model, for which an equivalent linear relaxation model is derived. Hysteretic properties can be encountered in engineering structures exposed to severe cyclic environmental loads, as well as in vibration mitigation devices, such as Magneto-Rheological (MR) dampers. The identification technique incorporates the equivalent linear damper model in the estimation procedure. Synthetic data, representing the random vibrations of systems with hysteresis, validate the estimated system parameters by the presented identification method at low and high-levels of excitation amplitudes.

System Identification of a Base-Isolated Bridge by Ambient and Forced Vibration Tests

Abstract Sciarapotamo Bridge, located in Reggio Calabria Province, Italy, has been recently retrofitted by replacing its deteriorated concrete bridge deck with a composite steel- concrete deck, and isolating the new deck with eight high damping rubber, and four multi-directional sliding bearings. Full-scale ambient and forced vibration dynamic commissioning tests were performed on the bridge just before the bridge has become operational. Three different output-only system identification methods with ambient vibration measurements were used for modal parameter identification, namely: (1) multiple reference natural excitation technique in conjunction with eigen-system realization algorithm, (2) enhanced frequency domain decomposition, and (3) data driven stochastic subspace identification methods. Modal parameter estimation results using different output-only identification methods were presented and compared within the paper. In addition, relatively higher level forced vibration test data was used for estimating frequency response functions, identifying isolated natural frequencies, and damping ratios of the retrofitted bridge in as-built condition. Estimated damping coefficients under different excitation levels are of great value, showing the total damping in the system at low level ambient and relatively higher level forced vibration tests. Experimentally obtained modal parameters of the bridge set the undamaged benchmark state of the bridge for future potential condition assessment studies.

Modal parameter estimation from optically-measured data using a hybrid output-only system identification method

The accuracy of estimated modal parameters using different output-only system identification techniques is dependent on the amplitude of the structural response and the associated measurement noise. Unlike, a typical experiment using attached sensors and a multi-channel data acquisition (DAQ) system, optical measurement systems can have high levels of measurement noise that may result in estimated modal parameters that have low accuracy. Although the BSS-based modal parameter estimation techniques are able to identify modal characteristics of the structures from system responses, the performance of these techniques are generally limited by the damping values of structures and the number of sensors mounted on the structure. This paper proposes a new hybrid output-only system identification method that improves the extraction of modal parameters from optically measured system responses. The proposed Operational Modal Analysis (OMA) method employs a BSS learning technique, referred to as Complexity Pursuit (CP), to recover the source signals (i.e. time-domain modal responses). Afterwards, the recovered time-domain modal responses were further processed using the poly-reference least square complex frequency domain (PLSCF) technique to accurately estimate modal information from the recovered source signals. In this work, the numerical response of a cantilevered beam is processed using the hybrid output-only system identification method to evaluate the accuracy of the proposed technique in identifying modal parameters in the presence of noise. Furthermore, the proposed method is used to characterize the optically measured dynamic response of a 2.3-m long wind turbine blade. The obtained results indicate that the proposed output-only system identification is robust to the measurement noise, and since the contribution of the other modal responses are attenuated after applying BSS the hybrid methodology has a potential to identify accurate dynamic characteristics of structures from optically measured data.

Structural Identification of an 18-Story RC Building in Nepal Using Post-Earthquake Ambient Vibration and Lidar Data

Few studies have been conducted to assess post-earthquake performance of structures using vibration measurements. This paper presents system identification and finite element modeling of an 18-story apartment building that was damaged during the 2015 Gorkha earthquake in Nepal. In July 2016, a few months after the earthquake, the authors visited the building and collected its ambient acceleration response. The recorded data are analyzed and the modal parameters of the structure are identified using an output-only system identification method. A linear finite element model of the building is also developed based on the geometry of the building and its material properties to estimate numerically its dynamic characteristics. The identified modal parameters are compared to those of the model to identify possible shortcomings of the modeling and identification approaches. The identified natural frequencies and mode shapes of the first two vibration modes are in good agreement with the model.

Identification of modal parameters based on moving load excitation

Abstract It is often desired to measure the model parameters of bridges, but normally the forcing function cannot be measured so it is necessary to use output-only system identification methods. A moving vehicle provides a force on a bridge that could be used for input-output analysis, which could be superior, but the force varies in space as well as time, so existing system identification methods are not directly applicable. To address this issue, this paper proposes a new strategy to use the moving load response to identify the modal parameters. A numerically simulated simply supported Euler-Bernoulli beam of known parameters is used as an example case to test the validity of the approach. Frequency Domain Decomposition is first implemented to extract the mode shapes from the simulated acceleration responses. Then, by applying the mode superposition method, the simulated force and acceleration responses are transformed into modal space. The accelerances of five modes are then processed using the Levenberg-Marquardt method such that the three unknown parameters, namely natural frequency, damping ratio, and modal mass, of each mode are determined simultaneously. The effectiveness of the proposed method is validated by the low percentage errors (less than 1.7%) for all three identified modal parameters compared to their actual values for four of the five modes.

가속도응답과 ICA 기법을 이용한 구조물의 모드특성 및 하중 동시추정기법

In this paper, a new system-force identification technique in frequency domain is proposed that is simultaneously to estimate the natural frequency, damping ratio and external modal load by back-calculation from the Kalman filter and the acceleration responses of building structure. The technique is a kind of output-only system identification method to predict the dynamic properties of governing modes separated by applying independent component analysis to the measured acceleration responses and then by minimizing the performance index cooperated with a power spectral density and its derivative of estimated modal load by Kalman filter and the corresponding modal responses. For the verification of the proposed method, a numerical simulation for SDOF system and an application for in-situ measurement data were performed. The results from the simulations show that the proposed technique can estimate the modal properties and modal load more precisely than a conventional output-only subspace identification technique. Because the damping ratio obtained by the proposed technique has a some variations depending on the number of sections for averaging and a duration time in the process of in-situ measurement, so it needs a profound research and additional verification process for more stable estimation of damping ratio.

Variability of Modal Parameter Estimations Using Two Different Output-Only System Identification Methods

Abstract Accurate damage identification in a structure depends on the accurate estimation of modal parameters; therefore, an important step in the vibration-based structural health monitoring process is the estimation of modal parameters. The purpose of this study was to investigate systematically the variability of identified modal parameters of a steel model bridge with low damping using simple statistical measures. In order to achieve this objective, first the modal parameters of an actual steel bridge were estimated using two different and widely used output-only system identification methods, the natural excitation technique with an eigensystem realization algorithm and enhanced frequency domain decomposition. Then a calibrated finite element model of the bridge was developed using the estimated modal parameters. Using the simulated data from the calibrated model, the variability of modal parameter estimations due to variability of the spatial sensor density, measurement/sensor noise, and response data length input factors was investigated. The input factors chosen are significant for the performance of the output-only system identification methods used and therefore are deemed important for accurate damage detection.

Uncertainty analysis of system identification results obtained for a seven-story building slice tested on the UCSD-NEES shake table

A full-scale seven-story reinforced concrete building section/slice was tested on the Network for Earthquake Engineering Simulation (NEES) shake table at the University of California San Diego during the period of October 2005 to January 2006. Three output-only system identification methods were used to extract the modal parameters (natural frequencies, damping ratios, and mode shapes) of the test structure at different damage states. In this study, the performance of these system identification methods is investigated in two cases: (Case I) when these methods are applied to the measured dynamic response of the structure and (Case II) when these methods are applied to the dynamic response of the structure simulated using a three-dimensional nonlinear finite element model thereof. In both cases, the uncertainty/variability of the identified modal parameters due to the variability of several input factors is quantified through analysis of variance (ANOVA). In addition to ANOVA, meta-models are used for effect screening in Case II (based on the simulated data), which also capture the effects of linear interactions of the input factors. The four input factors considered in Case I are amplitude of input excitation, spatial density of measurements, length of response data used for system identification, and model order used in the parametric system identification methods. In the second case of uncertainty analysis, in addition to these four input factors, measurement noise is also considered. The results show that for all three methods considered, the amplitude of excitation is the most significant factor explaining the variability of the identified modal parameters, especially the natural frequencies. Copyright © 2013 John Wiley & Sons, Ltd.

Ambient Vibration Testing for Story Stiffness Estimation of a Heritage Timber Building

This paper investigates dynamic characteristics of a historic wooden structure by ambient vibration testing, presenting a novel estimation methodology of story stiffness for the purpose of vibration-based structural health monitoring. As for the ambient vibration testing, measured structural responses are analyzed by two output-only system identification methods (i.e., frequency domain decomposition and stochastic subspace identification) to estimate modal parameters. The proposed methodology of story stiffness is estimation based on an eigenvalue problem derived from a vibratory rigid body model. Using the identified natural frequencies, the eigenvalue problem is efficiently solved and uniquely yields story stiffness. It is noteworthy that application of the proposed methodology is not necessarily confined to the wooden structure exampled in the paper.

Experimental and analytical system identification of Eynel arch type steel highway bridge

This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the Ayvacık county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat Uğurlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.

Output-Only System Identification of Posttensioned Segmental Concrete Highway Bridges

This paper discusses the application of system identification of a highway bridge using finite-element method and ambient-vibration testing. The posttensioned Gulburnu Highway Bridge located on the Giresun-Espiye state highway was selected as a case study. A finite-element model of the bridge was developed using SAP2000 software, and dynamic characteristics were obtained analytically. During the test, sources of ambient excitations were provided by the traffic effects over the bridge. Ambient-vibration tests were applied to the bridge to identify dynamic characteristics. The selection of measurement time, frequency span, and effective mode number was considered from similar studies in the literature. Two output-only system identification methods, enhanced frequency domain decomposition and stochastic subspace identification, were used to estimate the dynamic characteristics of the bridge experimentally. The accuracy and efficiency of both methods were investigated and compared with finite-element results....

Application of Modal Identification Methods to Spatial Structure Using Field Measurement Data

Modal identification with output-only measurements plays a key role in vibration-based damage detection, model updating, and structural health monitoring in civil engineering. This paper addresses the application of modal identification method to a triangle steel tube truss natatorium using the field measurement data. To obtain dynamic characteristics of the spatial structure, four different output-only system identification methods are employed. They are natural excitation technique–eigensystem realization algorithm, data-driven stochastic subspace identification method, frequency-domain decomposition/frequency-spatial domain decomposition method, and half spectra/rational fractional orthogonal polynomial method. First an analytical modal analysis was performed on the three-dimensional finite element model according to the factual layout design to obtain the calculated frequencies and mode shapes. Then the whole procedure of the field vibration tests on the natatorium was presented. Finally, practical issues and efficiency of the four output-only modal identification techniques are investigated, and compared with the results from a finite element model. The system identification results demonstrate that both methods can provide reliable information on dynamic characteristics of the spatial structure. The frequency-domain methods, however, can quickly identify the modal parameters, but the leakage error introduced by power-spectral density estimation is existent due to the limited length of data. And the time-domain methods can avoid the leakage error, but the computational modes and the computational cost are the main two drawbacks in application. The conclusion is that several system identification methods should be consulted to ensure the accuracy of the estimated modal parameters.