• Earthquakes and Structures
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• v.8 no.6
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• pp.1325-1348
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• 2015

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

• Smart Structures and Systems
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• v.25 no.2
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• pp.155-167
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• 2020

This paper demonstrates a real-time hybrid substructuring (RTHS) shake table test to evaluate the seismic performance of a base isolated building. Since RTHS involves a feedback loop in the test implementation, the frequency dependent magnitude and inherent time delay of the actuator dynamics can introduce inaccuracy and instability. The paper presents a robust stability and performance analysis method for the RTHS test. The robust stability method involves casting the actuator dynamics as a multiplicative uncertainty and applying the small gain theorem to derive the sufficient conditions for robust stability and performance. The attractive feature of this robust stability and performance analysis method is that it accommodates linearized modeled or measured frequency response functions for both the physical substructure and actuator dynamics. Significant experimental research has been conducted on base isolators and dampers toward developing high fidelity numerical models. Shake table testing, where the building superstructure is tested while the isolation layer is numerically modeled, can allow for a range of isolation strategies to be examined for a single shake table experiment. Further, recent concerns in base isolation for long period, long duration earthquakes necessitate adding damping at the isolation layer, which can allow higher frequency energy to be transmitted into the superstructure and can result in damage to structural and nonstructural components that can be difficult to numerically model and accurately predict. As such, physical testing of the superstructure while numerically modeling the isolation layer may be desired. The RTHS approach has been previously proposed for base isolated buildings, however, to date it has not been conducted on a base isolated structure isolated at the ground level and where the isolation layer itself is numerically simulated. This configuration provides multiple challenges in the RTHS stability associated with higher physical substructure frequencies and a low numerical to physical mass ratio. This paper demonstrates a base isolated RTHS test and the robust stability and performance analysis necessary to ensure the stability and accuracy. The tests consist of a scaled idealized 4-story superstructure building model placed directly onto a shake table and the isolation layer simulated in MATLAB/Simulink using a dSpace real-time controller.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.189-194
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• 2007

An experimental real-time hybrid method, which implements the wind response control of a building structure with only a two-way TLMD, is proposed and verified through a shaking table test. The building structure is divided into the upper experimental TLMD and the lower numerical structural part. The shaking table vibrates the TLMD with the response calculated from the numerical substructure, which is subjected to the excitations of the measured interface control force at its top story and an wind-load input at its base. The results show that the conventional method can be replaced by the proposed methodology with a simple installation and accuracy for evaluating the control performance of a TLMD.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.5
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• pp.485-495
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• 2008

An experimental real-time hybrid method, which implements the vibration control of a building structure with only a two-way TLMD, is proposed and verified through a shaking table test. The building structure is divided into the upper experimental TLMD and the lower numerical structural part. The shaking table vibrates the TLMD with the response calculated from the numerical substructure, which is subjected to the excitations of the measured interface control force at its top story and sinusoidal waves input at its base. The results show that the conventional method can be replaced by the proposed methodology with a simple installation and accuracy for evaluating the control performance of a TLMD.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.5
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• pp.11-24
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• 2011

A real-time hybrid test of a 3 story-3 bay reinforced concrete frame which is divided into numerical and physical substructure models under uniaxial earthquake excitation was run using a fixed iteration implicit HHT time integration method. The first story inner non-ductile column was selected as the physical substructure model, and uniaxial earthquake excitation was applied to the numerical model until the specimen failed due to severe damage. A finite-element analysis program, Mercury, was newly developed and optimized for a real-time hybrid test. The drift ratio based on the top horizontal displacement of the physical substructure model was compared with the result of a numerical simulation by OpenSees and the result of a shaking table test. The experiment in this paper is one of the most complex real-time hybrid tests, and the description of the hardware, algorithm and models is presented in detail. If there is an improvement in the numerical model, the evaluation of the tangent stiffness matrix of the physical substructure model in the finite element analysis program and better software to reduce the computational time of the element state determination for the force-based beam-column element, then the comparison with the results of the real-time hybrid test and the shaking table test deserves to make a recommendation. In addition, for the goal of a "Numerical simulation of the complex structures under dynamic loading", the real time hybrid test has enough merit as an alternative to dynamic experiments of large and complex structures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.443-453
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• 2013

The hybrid test is one of the most advanced test methods to predict the structural dynamic behavior with the interaction between a physical substructure and a numerical modeling in the hybrid control system. The purpose of this study is to perform the multi-directional dynamic test of a steel frame structure with the real-time hybrid system and to evaluate the validation of the results. In this study, FEAPH, nonlinear finite element analysis program for hybrid only, was developed and the hybrid control system was optimized. The inefficient computational time was improved with a fixed number iteration method and parallel computational techniques used in FEAPH. Furthermore, the previously used data communication method and the interface between a substructure and an analysis program were simplified in the control system. As the results, the total processing time in real-time hybrid test was shortened up to 10 times of actual measured seismic period. In order to verify the accuracy and validation of the hybrid system, the linear and nonlinear dynamic tests with a steel framed structure were carried out so that the trend of displacement responses was almost in accord with the numerical results. However, the maximum displacement responses had somewhat differences due to the analysis errors in material nonlinearities and the occurrence of permanent displacements. Therefore, if the proper material model and numerical algorithms are developed, the real-time hybrid system could be used to evaluate the structural dynamic behavior and would be an effective testing method as a substitute for a shaking table test.

• Structural Engineering and Mechanics
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• v.83 no.1
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• pp.93-108
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• 2022

Real-time hybrid simulation (RTHS) was applied to investigate the train-bridge interaction of a high-speed railway system, where the railway bridge was selected as the numerical substructure, and the train was physically tested. The interaction between the two substructures was reproduced by a servo-hydraulic shaking table. To accurately reproduce the high-frequency interaction responses ranging from 10-25Hz using the hydraulic shaking table with an inherent delay of 6-50ms, an adaptive time series (ATS) compensation algorithm combined with the linear quadratic Gaussian (LQG) was proposed and implemented in the RTHS. Testing cases considering different train speeds, track irregularities, bridge girder cross-sections, and track settlements featuring a wide range of frequency contents were conducted. The performance of the proposed ATS+LQG delay compensation method was compared to the ATS method and RTHS without any compensation in terms of residual time delays and root mean square errors between commands and responses. The effectiveness of the ATS+LQG method to compensate time delay in RTHS with high-frequency responses was demonstrated and the proposed ATS+LQG method outperformed the ATS method in yielding more accurate responses with less residual time delays.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.5 s.51
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• pp.99-106
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• 2006

The Real-Time Hybrid Test system presented in this paper is based on the pseudodynamic test method, and it combines physical testing with model-based simulation. The system is designed to achieve a rate of loading that is significantly higher than that of a conventional pseudodynamic test approaching the real-time response of a structure subjected to earthquake loads. To provide robust computation environment for the analysis of many degree-of-freedom structures, the system adopts an implicit time integration scheme in the model-based simulation. This paper presents an overview of the developed system and numerical simulations that were conducted to evaluate the performance of the computation scheme adopted here. Results of these studies have demonstrated the good performance of the computation scheme for real-time multiple-degree-of-freedom tests.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.2409-2421
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• 2011

This paper will present hybrid tests to a one bay-one story steel frame structure under ground excitation. A structure used in this paper for hybrid test, to evaluate performance and behavior, is divided into two models; one is numerical model with one column element, and a truss or a beam element, the other is physical substructural model with one beam-column element. All tests considered one or three degrees of freedom to implement real-time hybrid test, and two control algorithms to control hardware are used; one using MATLAB/Simulink, the other using OpenSees, OpenFresco and xPCTarget. In addition, for real-time data communication between numerical and physical substructural models SCRAMNet was used. The results of hybrid tests were compared with one of numerical analysis of numerical model with fiber force-based beam-column elements using OpenSees. Real-time hybrid tests were implemented for the validation of control system with simple structure, and then it will be extended to hybrid test for higher nonlinear or complex structure later on.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1247-1267
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• 2014

Real-Time Hybrid Simulation (RTHS) is a novel approach conceived to evaluate dynamic responses of structures with parts of a structure physically tested and the remainder parts numerically modelled. In RTHS, delay estimation is often a precondition of compensation; nonetheless, system delay may vary during testing. Consequently, it is sometimes necessary to measure delay online. Along these lines, this paper proposes an online delay estimation method using least-squares algorithm based on a simplified physical system model, i.e., a pure delay multiplied by a gain reflecting amplitude errors of physical system control. Advantages and disadvantages of different delay estimation methods based on this simplified model are firstly discussed. Subsequently, it introduces the least-squares algorithm in order to render the estimator based on Taylor series more practical yet effective. As a result, relevant parameter choice results to be quite easy. Finally in order to verify performance of the proposed method, numerical simulations and RTHS with a buckling-restrained brace specimen are carried out. Relevant results show that the proposed technique is endowed with good convergence speed and accuracy, even when measurement noises and amplitude errors of actuator control are present.