Large‐scale real‐time hybrid simulation involving multiple experimental substructures and adaptive actuator delay compensation

Real‐time hybrid simulation provides a viable method to experimentally evaluate the performance of structural systems subjected to earthquakes. The structural system is divided into substructures, where part of the system is modeled by experimental substructures, whereas the remaining part is modeled analytically. The displacements in a real‐time hybrid simulation are imposed by servo‐hydraulic actuators to the experimental substructures. Actuator delay compensation has been shown by numerous researchers to vitally achieve reliable real‐time hybrid simulation results. Several studies have been performed on servo‐hydraulic actuator delay compensation involving single experimental substructure with single actuator. Research on real‐time hybrid simulation involving multiple experimental substructures, however, is limited. The effect of actuator delay during a real‐time hybrid simulation with multiple experimental substructures presents challenges. The restoring forces from experimental substructures may be coupled to two or more degrees of freedom (DOF) of the structural system, and the delay in each actuator must be adequately compensated. This paper first presents a stability analysis of actuator delay for real‐time hybrid simulation of a multiple‐DOF linear elastic structure to illustrate the effect of coupled DOFs on the stability of the simulation. An adaptive compensation method then proposed for the stable and accurate control of multiple actuators for a real‐time hybrid simulation. Real‐time hybrid simulation of a two‐story four‐bay steel moment‐resisting frame with large‐scale magneto‐rheological dampers in passive‐on mode subjected to the design basis earthquake is used to experimentally demonstrate the effectiveness of the compensation method in minimizing actuator delay in multiple experimental substructures. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of peer‐to‐peer (P2P) internet online hybrid test system

A new Internet online hybrid test system, designated the ‘peer‐to‐peer (P2P) Internet online hybrid test system’, is proposed. In the system, the simulated structure is divided into multiple substructures, and each substructure is analysed numerically or tested physically in parallel at geographically distributed locations. The equations of motion are not formulated for the entire structure but for each substructure separately. Substructures are treated as highly independent systems, and only standard I/O, i.e. displacements and forces at the boundaries, are used as interfaces. A ‘Coordinator’ equipped with an iterative algorithm based on quasi‐Newton iterations is developed to achieve compatibility and equilibrium at boundaries. A test procedure, featuring two rounds of quasi‐Newton iterations and using assumed elastic stiffness, is adopted to avoid iteration for the substructure being tested physically. A fast and stable solution using a socket mechanism is developed for data exchange over the Internet. Demonstration tests applied to a base‐isolated structure was conducted, and the results are compared with an online hybrid test using the conventional test method. The results obtained from the P2P Internet hybrid test match very closely those obtained from the conventional tests. Investigations are also carried out on time consumption and control accuracy. The results show that the Internet data exchange solution using the socket mechanism is fast, and tests were completed successfully under the constructed Internet online hybrid test environment. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical characteristics of peer‐to‐peer (P2P) internet online hybrid test system and its application to seismic simulation of SRC structure

The peer‐to‐peer (P2P) Internet online hybrid test system has been developed for the seismic simulation of a structure. In this study, the stability and accuracy of the system are investigated analytically by studying the spectral radius of the recursive matrix of the test scheme featuring a two‐round quasi‐Newton test scheme. The applicability of the system is further examined by exploring the seismic responses of a complex structure, a steel‐encased reinforced concrete (SRC) structure with a steel tower on the top. The structure is divided into two numerical substructures and one tested part for hybrid test. The numerical substructures are simulated by sophisticated finite element method (FEM) models with material nonlinearities to capture local plastifications. Two types of FEM programs, namely OpenSEES and ABAQUS, which are suitable for the SRC part and the steel tower, respectively, are employed. The results demonstrate that the P2P system is able to simulate complex structures with significant nonlinearities. As compared with the previous study in which two elastic numerical substructures were considered, increase in the number of iterations in this study is not significant, because the associated nonlinearities are limited due to the small time interval adopted in the test. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance evaluation of a distributed hybrid test framework to reproduce the collapse behavior of a structure

A hybrid numerical and experimental simulation to collapse was conducted on a one‐half scale moment‐resisting frame building with two experimental substructures at different locations. An extensible hybrid test framework was used that adopts a generalized interface to encapsulate each numerical or tested substructure, through which only boundary displacements and forces are exchanged. Equilibrium and compatibility between substructures are enforced by an iterative quasi‐Newton procedure, while adopting a predictor‐and‐corrector method to avoid loading reversals on physically tested substructures. To overcome difficulties in controlling stiff axial and rotational deformations at the boundaries, the flexible test scheme employs either open‐loop or closed‐loop control at the boundaries: enforcing either compatibility or equilibrium, or both requirements at critical boundaries. The effectiveness of the extensible framework and its capability to simulate structural behavior through collapse is demonstrated by a geographically distributed test that reproduced the collapse behavior of a four‐story, two‐bay, steel moment frame previously tested on an earthquake simulator. A comparison of both experiments highlights the viability of the hybrid test as an effective tool for the performance evaluation of structural systems from the onset of damage through collapse. Copyright © 2011 John Wiley & Sons, Ltd.     

Collapse simulation of a four‐story steel moment frame by a distributed online hybrid test

The collapse of a one‐bay, four‐story steel moment frame is simulated in this study by the proposed peer‐to‐peer (P2P) Internet online hybrid test system. The typical beam hinging mechanism, which is ensured by a strong‐column, weak‐beam design, is reproduced. The plastic hinges at the column bases are taken as the experimental portions, while the superstructure is analyzed numerically by a general‐purpose finite element program. The implicit plastic rotations of the two column bases are treated as boundary displacements. In order to account for the complex behavior of the column bases, the P2P system is modified to use the secant stiffness during iterations, and the physical specimens are designed such that the plastic hinge behavior can be obtained. For this study, the three substructures are distributed to different locations. A large ground motion is repeatedly imposed until the column bases lose their capacity to sustain the gravity load. As a result, significant deterioration is observed at both column bases. The proposed P2P system is thus demonstrated to be able to accommodate multiple‐tested substructures involving unstable behavior. The results suggest that the P2P Internet online hybrid test system provides a reliable means of studying structures up to collapse. Copyright © 2008 John Wiley & Sons, Ltd.     

Linear‐elastic lateral load analysis and seismic design of pin‐supported wall‐frame structures with yielding dampers

This paper describes an analytical investigation on a reinforced concrete lateral load resisting structural system comprising a pin‐supported (base‐rocking) shear wall coupled with a moment frame on 1 or both sides of the wall. Yielding dampers are used to provide supplemental energy dissipation through the relative displacements at the vertical connections between the wall and the frames. The study extends a previous linear‐elastic model for pin‐supported wall‐frame structures by including the effects of the dampers. A closed‐form solution of the lateral load behavior of the structure is derived by approximating the discrete wall‐frame‐damper interactions with distributed (ie, continuous) properties. The validity of the model is verified by comparing the closed‐form results with computational models using OpenSees program. Then, a parametric analysis is conducted to investigate the effects of the wall, frame, and damper stiffness on the behavior of the structure. It is found that the damper stiffness significantly affects the distribution of shear forces and bending moments over the wall height. Finally, the performance‐based plastic design approach extended to the wall‐frame‐damper system is proposed. Case studies are carried out to design 2 damped pin‐supported wall‐frame structures using the proposed approach. Nonlinear dynamic time‐history analyses are conducted to verify the effectiveness of this method. Results indicate that the designed structures can achieve the performance level with the story drift ratios less than target values, and weak‐story failure mechanism is not observed. The approach can be used in engineering applications.     

Real‐time hybrid experiments with Newmark integration,MCSmd outer‐loop control and multi‐tasking strategies

Real‐time hybrid testing is a promising technique for experimental structural dynamics, in which the structure under consideration is split into a physical test of key components and a numerical model of the remainder. The physical test and numerical analysis proceed in parallel, in real time, enabling testing of critical elements at large scale and at the correct loading rate. To date most real‐time hybrid tests have been restricted to simple configurations and have used approximate delay compensation schemes. This paper describes a real‐time hybrid testing approach in which non‐linearity is permitted in both the physical and numerical models, and in which multiple interfaces between physical and numerical substructures can be accommodated, even when this results in very stiff coupling between actuators. This is achieved using a Newmark explicit numerical solver, an advanced adaptive controller known as MCSmd and a multi‐tasking strategy. The approach is evaluated through a series of experiments on discrete mass–spring systems. Copyright © 2006 John Wiley & Sons, Ltd.     

采用多种有限元子结构的混合试验系统

采用子结构混合实验方法进行复杂结构的地震响应模拟。在混合实验中,根据结构的特征划分为多个子结构,每个子结构被封装起来,只有边界上的力和位移作为子结构间相互作用的变量,利用拟牛顿法保持整体结构的平衡和协调。目标结构为SRC框架剪力墙结构体系,结构顶部设置11层高的钢塔。在混合实验中,该结构被分为3个子结构,SRC部分为第一个子结构,采用OpenSees进行模拟;钢塔的第1层比较薄弱,是变形集中区域,采用实验进行模拟;钢塔其余部分采用ABAQUS有限元程序进行模拟。实验得到准确的地震响应,表明本文提出的混合实验方法可有效地结合多个有限元程序,充分利用各个有限元程序的优点进行复杂结构的地震响应模拟。     

Flexible substructure online hybrid test system using conventional testing devices

This paper presents a substructure online hybrid test system that is extensible for geographically distributed tests.This system consists of a set of devices conventionally used for cyclic tests to load the tested substructures onto the target displacement or the target force.Due to their robustness and portability,individual sets of conventional loading devices can be transported and reconfigured to realize physical loading in geographically remote laboratories.Another appealing feature is the flexible displacement-force mixed control that is particularly suitable for specimens having large disparities in stiffness during various performance stages.To conduct a substructure online hybrid test,an extensible framework is developed,which is equipped with a generalized interface to encapsulate each substructure.Multiple tested substructures and analyzed substructures using various structural program codes can be accommodated within the single framework,simply interfaced with the boundary displacements and forces.A coordinator program is developed to keep the boundaries among all substructures compatible and equilibrated.An Internet-based data exchange scheme is also devised to transfer data among computers equipped with different software environments.A series of online hybrid tests are introduced,and the portability,flexibility,and extensibility of the online hybrid test system are demonstrated.     

Stability analysis of MDOF real‐time dynamic hybrid testing systems using the discrete‐time root locus technique

The time delay resulting from the servo hydraulic systems can potentially destabilize the real‐time dynamic hybrid testing (RTDHT) systems. In this paper, the discrete‐time root locus technique is adopted to investigate the delay‐dependent stability performance of MDOF RTDHT systems. Stability analysis of an idealized two‐story shear frame with two DOFs is first performed to illustrate the proposed method. The delay‐dependent stability condition is presented for various structural properties, time delay, and integration time steps. Effects of delay compensation methods on stability are also investigated. Then, the proposed method is applied to analyze the delay‐dependent stability of a single shaking table RTDHT system with an 18‐DOF finite element numerical substructure, and corresponding RTDHTs are carried out to verify the theoretical results. Furthermore, the stability behavior of a finite element RTDHT system with two physical substructures, loaded by twin shaking tables, is theoretically and experimentally investigated. All experimental results convincingly demonstrate that the delay‐dependent stability analysis on the basis of the discrete‐time root locus technique is feasible. Copyright © 2014 John Wiley & Sons, Ltd.     

Modified state–space procedures for pseudodynamic testing

The existing on‐line numerical integration algorithms are derived from the Newmark method, which is based on an approximation of derivatives in the differential equation. The state–space procedure (SSP), based on an interpolation of the discrete excitation signals for piecewise convolution integral, has been confirmed as more reliable than the Newmark method in terms of numerical accuracy and stability. In an attempt to enhance the pseudodynamic test, this study presents an on‐line integration algorithm (referred to as the OS–SSP method) via an integration of the state–space procedure with Nakashima's operator‐splitting concept. Numerical stability and accuracy assessment of the proposed algorithm in addition to the explicit Newmark method and the OS method were investigated via an eigenvalue, frequency‐domain and time‐domain analysis. Of the on‐line integration algorithms investigated, the OS–SSP method is demonstrated as the most accurate method with an acceptable stability (although not unconditionally stable) characteristic. Therefore, the OS–SSP method is the most desirable method for pseudodynamic testing if the numerical stability criterion (Δt/T⩽0.5) is ensured for every vibration mode involved. Copyright © 2001 John Wiley & Sons, Ltd.     

Online hybrid test by internet linkage of distributed test‐analysis domains

Online hybrid tests (called the online tests), particularly when combined with substructuring techniques, are able to conduct large‐scale tests. An extension of this technique is to combine multiple loading tests conducted in remote locations and to integrate the tests with large numerical analysis codes. In this study, a new Internet online test system is developed in which a physical test is conducted in one place, the associated numerical analysis is performed in a remote location, and the two locations communicate over the Internet. To implement the system, a technique that links test and analysis domains located at different places is proposed, and an Internet data exchange interface is devised to allow data communication across Internet. A practical method that utilizes standard protocols implemented by operating systems for sharing files and folders is adopted to ensure stable and robust communication between remotely located servers that commonly protect themselves by strict firewalls. To combine the online test with a finite element program formulated in an incremental form and adopting an implicit integration scheme, a tangent stiffness prediction procedure is proposed. In this procedure, a tangent stiffness is estimated based on a few previous steps of experimental data. Using the system devised, tests on a base‐isolated structure were carried out. Here, the base‐isolation layer was taken as the tested part and tested in Kyoto University, Japan, and the superstructure was modelled by means of a finite element program and analysed in a computer located in Osaka University. A series of physical Internet online tests were carried out, with the integration time interval and the method of tangent stiffness prediction as the major parameters. The tests demonstrated that the Internet communication was very stable and robust, without malfunctions. The proposed method of stiffness prediction was effective even when the experimental hysteresis curves exhibited complex behaviour, thereby ensuring accurate simulation for the earthquake response of the entire structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Hybrid simulation of a zipper‐braced steel frame under earthquake excitation

Hybrid simulation is a testing methodology that combines laboratory and analytical simulation to evaluate seismic response of complex structural framing systems. One or more portions of the structure, which may be difficult to model numerically or have properties that have not been examined before, are tested in one or more laboratories, whereas the remainder of the structure is modeled in software using one or more computers. These separate portions are assembled such that combined dynamic response of the hybrid model to excitation is computed using a time‐stepping procedure. A hybrid simulation conducted to examine the seismic response of a type of steel concentrically braced frame, the suspended‐zipper‐braced frame, is presented. The hybrid simulation testing architecture, hybrid model, test setup, solution algorithm, and the seismic response of the suspended‐zipper‐braced frame hybrid model are discussed. Accuracy of this hybrid simulation is examined by comparing hybrid and computer‐only simulations and the errors are quantified using an energy‐based approach. This comparison indicates that the deployed hybrid simulation method can be used to accurately model the seismic response of a complex structural system such as the zipper‐braced frame. Copyright © 2008 John Wiley & Sons, Ltd.     

Test on full‐scale three‐storey steel moment frame and assessment of ability of numerical simulation to trace cyclic inelastic behaviour

A test on a full‐scale model of a three‐storey steel moment frame was conducted, with the objectives of acquiring real information about the damage and serious strength deterioration of a steel moment frame under cyclic loading, studying the interaction between the structural frame and non‐structural elements, and examining the capacity of numerical analyses commonly used in seismic design to trace the real cyclic behaviour. The outline of the test structure and test program is presented, results on the overall behaviour are given, and correlation between the experimental results and the results of pre‐test and post‐test numerical analyses is discussed. Pushover analyses conducted prior to the test predicted the elastic stiffness and yield strength very reasonably. With proper adjustment of strain hardening after yielding and composite action, numerical analyses were able to accurately duplicate the cyclic behaviour of the test structure up to a drift angle of 1/25. The analyses could not trace the cyclic behaviour involving larger drifts in which serious strength deterioration occurred due to fracture of beams and anchor bolts and progress of column local buckling. Copyright © 2005 John Wiley & Sons, Ltd.     

Modified predictor–corrector numerical scheme for real‐time pseudo dynamic tests using state‐space formulation

This paper deals with an explicit numerical integration method for real‐time pseudo dynamic tests. The proposed method, termed the MPC‐SSP method, is suited to use in real‐time pseudo dynamic tests as no iteration steps are involved in each step of computation. A procedure for implementing the proposed method in real‐time pseudo dynamic tests is described in the paper. A state‐space approach is employed in this study to formulate the equations of motion of the system, which is advantageous in real‐time pseudo dynamic testing of structures with active control devices since most structural control problems are formulated in state space. A stability and accuracy analysis of the proposed method was performed based on linear elastic systems. Owing to an extrapolation scheme employed to predict the system's future response, the MPC‐SSP method is conditionally stable. To demonstrate the effectiveness of the MPC‐SSP method, a series of numerical simulations were performed and the performance of the MPC‐SSP method was compared with other pseudo dynamic testing methods including Explicit Newmark, Central Difference, Operator Splitting, and OS‐SSP methods based on both linear and non‐linear single‐degree‐of‐freedom systems. Copyright © 2004 John Wiley & Sons, Ltd.     

Improved risk‐targeted performance‐based seismic design of reinforced concrete frame structures

This paper presents a procedure for seismic design of reinforced concrete structures, in which performance objectives are formulated in terms of maximum accepted mean annual frequency (MAF) of exceedance, for multiple limit states. The procedure is explicitly probabilistic and uses Cornell's like closed‐form equations for the MAFs. A gradient‐based constrained optimization technique is used for obtaining values of structural design variables (members' section size and reinforcement) satisfying multiple objectives in terms of risk levels. The method is practically feasible even for real‐sized structures thanks to the adoption of adaptive equivalent linear models where element‐by‐element stiffness reduction is performed (2 linear analyses per intensity level). General geometric and capacity design constraints are duly accounted for. The procedure is applied to a 15‐storey plane frame building, and validation is conducted against results in terms of drift profiles and MAF of exceedance, obtained by multiple‐stripe analysis with records selected to match conditional spectra. Results show that the method is suitable for performance‐based seismic design of RC structures with explicit targets in terms of desired risk levels.     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

A Rosenbrock‐W method for real‐time dynamic substructuring and pseudo‐dynamic testing

A variant of the Rosenbrock‐W integration method is proposed for real‐time dynamic substructuring and pseudo‐dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic behaviour of hybrid systems made of PR composite frames coupled with dissipative bracings

The paper investigates the dynamic behaviour of hybrid systems made of partially restrained (PR) steel–concrete composite frames coupled with viscoelastic dissipative bracings. A numerical model that accounts for both the resisting mechanisms of the joint and the viscoelastic contribution of the dissipative bracing is introduced and briefly discussed. The model is first validated against experimental outcomes obtained on a one‐storey two‐bay composite frame with partial strength semi‐rigid joints subjected to free vibrations. A number of time‐history analyses under different earthquake ground motions and peak ground accelerations are then carried out on the same type of frame. The purpose is to investigate the influence of the type of beam‐to‐column connection and property of the viscoelastic bracing on the performance of the hybrid system. The inherent stiffness of the bare PR frame and the plastic hysteresis of the beam‐to‐column joints, which always lead to only limited damage in the joint, are found to provide a significant contribution to the overall structural performance even under destructive earthquakes. This remark leads to the conclusion that the viscoelastic bracing can be effectively used within the hybrid system. Copyright © 2008 John Wiley & Sons, Ltd.     

Model‐based predicting and correcting algorithms for substructure online hybrid tests

A set of algorithms combined with a substructure technique is proposed for an online hybrid test framework, in which the substructures are encapsulated by a standard interface that implements displacements and forces at the common substructure boundaries. A coordinator equipped with the proposed algorithms is designed to achieve boundary compatibility and equilibrium, thereby endowing the substructures the ability to behave as one piece. A model‐based predictor and corrector, and a noniterative procedure, characterize the set of algorithms. The coordinator solves the dynamics of the entire structure and updates the static boundary state simultaneously by a quasi‐Newton procedure, which gradually formulates the condensed stiffness matrix associated with corresponding degrees of freedom. With the condensed stiffness matrix and dynamic information, a condensed equation of motion is derived and then solved by a typical time integration algorithm. Three strategies for updating the condensed stiffness matrix are incorporated into the proposed algorithms. Each adopts different stiffness matrix during the predicting and correcting stage. These algorithms are validated by two numerical substructure simulations and a hybrid test. The effectiveness and feasibility are fully demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.