Time domain system identification of unknown initial conditions
Ming-Hsiang Shih2004, Journal of Zhejiang University Science
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
System identification is a method for using measured data to create or improve a mathematical model of the object being tested. From the measured data however, noise is noticed at the beginning of the response. One solution to avoid this noise problem is to skip the noisy data and then use the initial conditions as active parameters, to be found by using the system identification process. This paper describes the development of the equations for setting up the initial conditions as active parameters. The simulated data and response data from actual shear buildings were used to prove the accuracy of both the algorithm and the computer program, which include the initial conditions as active parameters. The numerical and experimental model analysis showed that the value of mass, stiffness and frequency were very reasonable and that the computed acceleration and measured acceleration matched very well.
Related papers
System identification of high-rise buildings using shear-bending model and ARX model: Experimental investigation
Earthquakes and Structures
System identification is regarded as the most basic technique for structural health monitoring to evaluate structural integrity. Although many system identification techniques extracting mode information (e.g., mode frequency and mode shape) have been proposed so far, it is also desired to identify physical parameters (e.g., stiffness and damping). As for high-rise buildings subjected to long-period ground motions, system identification for evaluating only the shear stiffness based on a shear model does not seem to be an appropriate solution to the system identification problem due to the influence of overall bending response.
Advanced System Identification for High-Rise Building Using Shear-Bending Model
Frontiers in Built Environment, 2016
In order to identify physical model parameters of a high-rise building, a new story stiffness identification method is presented based on a shear-bending model and the identification function. Although a shear building model may be the simplest conventional model for representing tall buildings, the system identification (SI) method using that model is not necessarily appropriate. This is because the influence of bending deformation is predominant in such high-rise buildings. For this reason, a shear-bending model is used where the shear and bending stiffnesses are unknown. In the previous researches using the shear-bending model, it was difficult to identify the bending stiffnesses stably and reliably. In this paper, to overcome such instability of bending stiffness identification of the shear-bending model, a new SI algorithm using both the shear model and the shearbending model is presented. The proposed SI algorithm is based on the observation that the fundamental-mode shape of the identified shear model is similar to that of the shear-bending model identified in the previous SI method. In order to verify the advanced SI method, two different 20-story building models are investigated in the numerical simulations. From the results of the simulations, both the shear and bending stiffnesses of the shear-bending model are identified reliably and stably in the proposed SI method.
A time domain based mechanical system identification
The present work presents a time domain based identification technique within the inverse problems scope. Here the set of unknown parameters which characterizes the mechanical behaviour of the system is identified by means of the minimization of a suitable error function which includes time domain data from both the real system and its respective mathematical model. The technique takes into account the constraint associated to the system evolution equations as being part of an extended error function what naturally gives rise to the Lagrange multiplier variables which are obtained via solution of an adjoint problem. Mechanical modelling plays a crucial role here inasmuch as once one has decided which unknown parameters influence the system response, they are used to parameterize the mass, stiffness and damping matrices of the system. The effectiveness of the technique is assessed by using experimental data which was collected from a pinned-pinned steel beam instrumented with four piezoelectric accelerometers and an electro-mechanical shaker. The parameters which have been chosen to be identified were: localized damping at the bearings, the first three damping factors of the structure and a localized mass associated to the interaction between the structure and the shaker.
Identification of Torsionally Coupled Shear Buildings Models Using a Vector Parameterization
Shock and Vibration, 2016
A methodology to estimate the shear model of seismically excited, torsionally coupled buildings using acceleration measurements of the ground and floors is presented. A vector parameterization that considers Rayleigh damping for the building is introduced that allows identifying the stiffness/mass and damping/mass ratios of the structure, as well as their eccentricities and radii of gyration. This parameterization has the advantage that its number of parameters is smaller than that obtained with matrix parameterizations or when Rayleigh damping is not used. Thus, the number of spectral components of the excitation signal required to identity the structural parameters is reduced. To deal with constant disturbances and measurement noise that corrupt acceleration measurements, Linear Integral Filters are used that guarantee elimination of constant disturbances and attenuation of noise.
Story-wise system identification of actual shear building using ambient vibration data and ARX model
Earthquakes and Structures
A sophisticated story-wise stiffness identification method for a shear building structure is applied to the case where the shear building is subjected to an actual micro-tremor. While the building responses to earthquake ground motions are necessary in the previous method, it is shown that micro-tremors can be used for identification within the same framework. This enhances the extended usability and practicality of the previously proposed identification method. The difficulty arising in the limit manipulation at zero frequency in the previous method is overcome by introducing an ARX model. The weakness of small SN ratios in the low frequency range is avoided by using the ARX model together with filtering and introducing new constraints on the ARX parameters.
System identification of super high-rise buildings using limited vibration data during the 2011 Tohoku (Japan) earthquake
Structural Control and Health Monitoring, 2012
A new method of system identification of high-rise buildings is proposed in which high-rise buildings are represented by a shear-bending model. The method is devised to find the story shear and bending stiffnesses of a specific story from the horizontal floor accelerations. The special characteristic of the proposed method is to use a previously derived set of closed-form expressions for the story shear and bending stiffnesses in terms of the limited floor accelerations and to utilize a reduced shear-bending model with the same number of elements as the vibration recording points. In the proposed method, a difficulty of prediction of an unstable specific function in a low frequency range can be overcome by introducing an ARX model. It is demonstrated that the shear-bending model can simulate the vibration records with a reasonable accuracy. It is shown further that the vibration records at two super high-rise buildings during the 2011 Tohoku (Japan) earthquake can be simulated with the proposed method including a technique of adding degrees of freedom between the vibration recording points.
Stiffness-damping simultaneous identification of buildings including unknown inner vibration source
Journal of Structural and Construction Engineering (Transactions of AIJ)
In this paper, a new stiffness-damping simultaneous identification method for a building structure is proposed when the building includes an unknown inner vibration source. The feature of this method is that the present identification can be performed even though the location and time-history of the vibration source in addition to all stiffness and damping coefficients are unknown. By performing limit manipulation, the relations between stiffnesses of consecutive stories and those between damping coefficients of consecutive stories can be obtained from the acceleration data at the floors just above and below the object story which can be recorded by using at least two sensors.
Simultaneous parameter and state estimation of shear buildings
Mechanical Systems and Signal Processing, 2016
This paper proposes an adaptive observer that simultaneously estimates the damping/ mass and stiffness/mass ratios, and the state of a seismically excited building. The adaptive observer uses only acceleration measurements of the ground and floors for both parameter and state estimation; it identifies all the parameter ratios, velocities and displacements of the structure if all the floors are instrumented; and it also estimates the state and the damping/mass and stiffness/mass ratios of a reduced model of the building if only some floors are equipped with accelerometers. This observer does not resort to any particular canonical form and employs the Least Squares (LS) algorithm and a Luenberger state estimator. The LS method is combined with a smooth parameter projection technique that provides only positive estimates, which are employed by the state estimator. Boundedness of the estimate produced by the LS algorithm does not depend on the boundedness of the state estimates. Moreover, the LS method uses a parametrization based on Linear Integral Filters that eliminate offsets in the acceleration measurements in finite time and attenuate high-frequency measurement noise. Experimental results obtained using a reduced-scale five-story confirm the effectiveness of the proposed adaptive observer.
Application of Story-Wise Shear Building Identification Method to Actual Ambient Vibration
Frontiers in Built Environment, 2015
Fujita K, Ikeda A and Takewaki I (2015) Application of story-wise shear building identification method to actual ambient vibration. Front. Built Environ. 1:2.
System identification of a super high-rise building via a stochastic subspace approach
A new method of system identification of high-rise buildings is proposed in which high-rise buildings are represented by a shear-bending model. The method is devised to find the story shear and bending stiffnesses of a specific story from the horizontal floor accelerations. The special characteristic of the proposed method is to use a previously derived set of closed-form expressions for the story shear and bending stiffnesses in terms of the limited floor accelerations and to utilize a reduced shear-bending model with the same number of elements as the vibration recording points. In the proposed method, a difficulty of prediction of an unstable specific function in a low frequency range can be overcome by introducing an ARX model. It is demonstrated that the shear-bending model can simulate the vibration records with a reasonable accuracy. It is shown further that the vibration records at two super high-rise buildings during the 2011 Tohoku (Japan) earthquake can be simulated with the proposed method including a technique of adding degrees of freedom between the vibration recording points.
Related papers
Stiffness-damping simultaneous identification using limited earthquake records
Earthquake Engineering & Structural Dynamics, 2000
A new method of sti!ness-damping simultaneous identi"cation of building structures is proposed using limited earthquake records. It is shown that when horizontal accelerations are recorded at the #oors just above and below a speci"c storey in a shear building model, the storey sti!ness and the damping ratio can be identi"ed uniquely. The viscous damping coe$cient and the linear hysteretic damping ratio can also be identi"ed simultaneously in a numerical model structure. The accuracy of the present identi"cation method is investigated through the actual limited earthquake records in a base-isolated building. It is further shown that an advanced identi"cation technique for mechanical properties of a Maxwell-type model can be developed by combining the present method with a perturbation technique.
An Iterative Algorithm for Noise Reduction in the System Identification of Shear Structures
The objective of this work was to reduce the noise adverse effect on the "System Identification" (SI) of linear shear structures. Taking into account the fundamental and significant effect of noise attenuation in boosting the levels of precision and the correctness of SI, the proposed method facilitates direct noise attenuation in the domain of time in parallel with the identification of structural system. Since in such fields as "Damage Detection" in structures, identification of the system's characteristic matrices is of the same importance as the identification of the frequency characteristics, or even more, the proposed method tries to identify the matrices of mass, damping and stiffness of shear structures. Efficiency and precision of the method have been examined through application of "closed loop solution" to two structures with analytical model.
Model updating of multistory shear buildings for simultaneous identification of mass, stiffness and damping matrices using two different soft-computing methods
Expert Systems With Applications an International Journal, 2011
In this research, two novel methods for simultaneous identification of mass-damping-stiffness of shear buildings are proposed. The first method presents a procedure to estimate the natural frequencies, modal damping ratios, and modal shapes of shear buildings from their forced vibration responses. To estimate the coefficient matrices of a state-space model, an auto-regressive exogenous excitation (ARX) model cooperating with a neural network concept is employed. The modal parameters of the structure are then evaluated from the eigenparameters of the coefficient matrix of the model. Finally, modal parameters are used to identify the physical/structural (i.e., mass, damping, and stiffness) matrices of the structure. In the second method, a direct strategy of physical/structural identification is developed from the dynamic responses of the structure without any eigenvalue analysis or optimization processes that are usually necessary in inverse problems. This method modifies the governing equations of motion based on relative responses of consecutive stories such that the new set of equations can be implemented in a cluster of artificial neural networks. The number of neural networks is equal to the number of degree-of-freedom of the structure. It is shown the noise effects may partially be eliminated by using high-order finite impulse response (FIR) filters in both methods. Finally, the feasibility and accuracy of the presented model updating methods are examined through numerical studies on multistory shear buildings using the simulated records with various noise levels. The excellent agreement of the obtained results with those of the finite element models shows the feasibility of the proposed methods.
System Identification Study of a 7-Story Full-Scale Building Slice Tested on the UCSD-NEES Shake Table
Journal of Structural Engineering, 2011
A full-scale seven-story reinforced concrete building slice was tested on the unidirectional UCSD-NEES shake table during the period October 2005 -January 2006. A rectangular wall acted as the main lateral force resisting system of the building slice. The shake table tests were designed to damage the building progressively through four historical earthquake records. The objective of the seismic tests was to validate a new displacement-based design methodology for reinforced concrete shear wall building structures. At several levels of damage, ambient vibration tests and low amplitude white noise base excitations tests were applied to the building which responded as a quasi-linear system with dynamic parameters evolving as a function of structural damage. Six different state-of-the-art system identification algorithms including three output-only and three input-output methods were used to estimate the modal parameters (natural frequencies, damping ratios, and mode shapes) at different damage levels based on the response of the building to ambient as well as white noise base excitations, measured using DC-coupled accelerometers. The modal parameters estimated at various damage 2 levels using different system identification methods are compared in order to: (1) validate/crosscheck the modal identification results and study the performance of each of these system identification methods, and (2) investigate the sensitivity of the identified modal parameters to actual structural damage. For a given damage level, the modal parameters identified using different methods are found to be in good agreement indicating that these estimated modal parameters are likely to be close to the actual modal parameters of the building specimen.
System Identification Study of a Seven-Story Full-Scale Building Slice Tested on the UCSD-NEES Shake Table
Journal of Structural Engineering, 2011
A full-scale seven-story reinforced concrete building slice was tested on the unidirectional UCSD-NEES shake table during the period October 2005 -January 2006. A rectangular wall acted as the main lateral force resisting system of the building slice. The shake table tests were designed to damage the building progressively through four historical earthquake records. The objective of the seismic tests was to validate a new displacement-based design methodology for reinforced concrete shear wall building structures. At several levels of damage, ambient vibration tests and low amplitude white noise base excitations tests were applied to the building which responded as a quasi-linear system with dynamic parameters evolving as a function of structural damage. Six different state-of-the-art system identification algorithms including three output-only and three input-output methods were used to estimate the modal parameters (natural frequencies, damping ratios, and mode shapes) at different damage levels based on the response of the building to ambient as well as white noise base excitations, measured using DC-coupled accelerometers. The modal parameters estimated at various damage 2 levels using different system identification methods are compared in order to: (1) validate/crosscheck the modal identification results and study the performance of each of these system identification methods, and (2) investigate the sensitivity of the identified modal parameters to actual structural damage. For a given damage level, the modal parameters identified using different methods are found to be in good agreement indicating that these estimated modal parameters are likely to be close to the actual modal parameters of the building specimen.
System identification in nonlinear structural seismic dynamics
Computer Methods in Applied Mechanics and …, 1975
This paper deals with the development of efficient identification methods for the determination of parameters associated with the nonlinear response of structural systems subject to seismic conditions. The equation of motion of the system is given by
Uncertainty analysis of system identification results obtained for a seven-story building slice tested on the UCSD-NEES shake table
Structural Control and Health Monitoring, 2013
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.
Response features and parametric identification of shear-deformation buildings with continuous–discrete modeling
Engineering Structures, 2014
This study presents fundamental response features of seismic shear motion in multi-story buildings with a continuous-discrete model and its degenerated ones, and shows their applications in inverse parametric identification. In particular, the building is modeled as a series of continuous shear-beams for interstory columns/walls and discrete lumped-masses for rigid floors. Shear motion response at one location of the building is then obtainable to an impulsive motion at another location in the time and frequency domains, termed here as generalized impulse and frequency response functions (GIRF and GFRF). The GIRF and GFRF are not only fundamental in relating seismic responses at the two locations of a building structure subjected to ground seismic excitation that is not fully known due to the complicated soilstructure interaction. They also play a key role in characterizing structural responses, as well as in identifying dynamic parameters of the building. For illustration, this study examines response features of ten-story building of Millikan Library in Pasadena, California with the Yorba Linda earthquake of September 3, 2002. With the use of the continuousdiscrete model as well as its degenerated ones, structural responses are interpreted from the perspective of wave propagation, and more importantly validated with the pertinent recordings and discrete-modelbased results. Parametric identification of the building with a pair of seismic recordings is then presented. This study finally comes up a conclusion that the proposed approach with continuous-discrete modeling is efficient and robust in forward predicting analysis and inverse system identification.
THE IDENTIFICATION OF BUILDING STRUCTURAL SYSTEMS II. THE NONLINEAR CASE
This paper models a building structure as a nonlinear feedback system and studies the effects of such a system model on the structural response to strong ground shaking. Nonlinear kernels arising in the identification procedure have been investigated and an error analysis presented. Applications of the Weiner method in studying the response of a reinforced concrete structure to strong ground shaking have been illustrated. The nature of the second order kernels has been displayed and the nonlinear contribution to the response at the roof level, during strong ground shaking, has been determined.
Frequency-Domain Physical-Parameter System Identification of Building Structures with Stiffness Eccentricity
Frontiers in Built Environment
A frequency-domain method of physical-parameter system identification is developed for three-dimensional building structures with stiffness eccentricity. Equations of motion in the time domain are transformed into the frequency domain. The dynamic equilibrium of the free body above the j-th story is used to identify the j-th story stiffness and damping. It is required to measure the horizontal and rotational accelerations at all stories to identify the story stiffness and damping coefficients of all stories. Compared to the previous approach using the special identification function, the limit manipulation at zero frequency is unnecessary and is robust for noise. Furthermore, it should be remarked that the quantities of eccentricities in all stories can be identified using the slopes of the functions for torsional stiffness identification in the frequency domain.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.