Numerical characteristics of the full operator hybrid simulation method

The full operator method (FOM) has been proposed to overcome some of the shortcomings of the commonly used operator splitting method (OSM). In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the tested structure. The numerical characteristics of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of the strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reasonably accurate results despite the presence of strong structural nonlinearity and displacement control errors.     

Iterative implicit integration procedure for hybrid simulation of large nonlinear structures

A fully implicit iterative integration procedure is presented for local and geographically distributed hybrid simulation of the seismic response of complex structural systems with distributed nonlinear behavior. The purpose of this procedure is to seamlessly incorporate experimental elements in simulations using existing fully implicit integration algorithms designed for pure numerical simulations. The difficulties of implementing implicit integrators in a hybrid simulation are addressed at the element level by introducing a safe iteration strategy and using an efficient procedure for online estimation of the experimental tangent stiffness matrix. In order to avoid physical application of iterative displacements, the required experimental restoring force at each iteration is estimated from polynomial curve fitting of recent experimental measurements. The experimental tangent stiffness matrix is estimated by using readily available experimental measurements and by a classical diagonalization approach that reduces the number of unknowns in the matrix. Numerical and hybrid simulations are used to demonstrate that the proposed procedure provides an efficient method for implementation of fully implicit numerical integration in hybrid simulations of complex nonlinear structures. The hybrid simulations presented include distributed nonlinear behavior in both the numerical and experimental substructures. Copyright © 2010 John Wiley & Sons, Ltd.     

A method for estimating specimen tangent stiffness for hybrid simulation

Researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness matrix of a test specimen in hybrid simulations employing implicit and mixed‐integration schemes. However, the computation of the tangent stiffness matrix during testing has proved to be challenging, particularly for test specimens with more than one degree of freedom (dof). This paper presents a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi‐dof test specimen. The proposed method is combined with the operator‐splitting method (OSM), and the capabilities, advantages and limitations of the new formulation are demonstrated through several examples. The accuracy, stability, and error propagation characteristics of the modified OSM are also studied theoretically as well as numerically. The research results show that the proposed algorithm provides results that are better than those produced via the regular OSM alone, especially for damped structures undergoing highly inelastic behavior during testing. Copyright © 2008 John Wiley & Sons, Ltd.     

A Self-tuning Robust Control System for nonlinear real-time hybrid simulation

In a real-time hybrid simulation, a transfer system is used to enforce the interface interaction between computational and physical substructures. A model-based, multilayer nonlinear control system is developed to accommodate extensive performance variations and uncertainties in a physical substructure. The aim of this work is to extend the application of real-time hybrid simulation to investigating failure, nonlinearity, and nonstationary behavior. This Self-tuning Robust Control System (SRCSys) consists of two layers: robustness and adaptation. The robustness layer synthesizes a nonlinear control law such that the closed-loop dynamics perform as intended under a broad range of parametric and nonparametric uncertainties. Sliding mode control is employed as the control scheme in this layer. Then, the adaptation layer reduces uncertainties at run time through slow and controlled learning of the control plant. The tracking performance of the SRCSys is evaluated in two experiments that have highly uncertain physical specimens.     

大空间地下结构地震响应混合试验研究

基于OpenSees-OpenFresco-MTS混合试验系统,选取关键构件底层中柱,进行大空间地下结构地震响应混合试验研究。在混合试验过程中,取结构底层中柱为试验子结构,取结构剩余部分与土体为数值子结构。为了满足试验要求,开发了一种专用于混合试验的可变刚度钢构件。通过更换柱脚螺杆改变试验装置侧向刚度。在混合试验前,根据数值模型中对应单元侧向刚度确定钢构件侧向刚度;根据幅值比和相位差等频域指标评价混合试验结果。试验结果显示:在上海人工波工况、El Centro波工况和Kobe波工况中,理论结果与试验结果匹配良好。在以大空间地下结构地震响应为研究对象时,基于OpenSees-OpenFresco-MTS的混合试验系统具有良好的稳定性与精确性。     

Test and numerical simulation of a new type of hybrid control technique

In this paper, a new hybrid control technique, based on a combination of base-isolation and semi-active variable stiffness/damping in a superstructure, is presented. To illustrate the efficiency of the proposed control system, model tests on a mini-electromagnetic shaking table and a numerical simulation were performed. The test and numerical calculation results indicate that this new hybrid control mode with additional damping and smaller additional stiffness can achieve a better control efficiency.     

Model updating method for substructure pseudo‐dynamic hybrid simulation

Substructure hybrid simulation has been actively investigated and applied to evaluate the seismic performance of structural systems in recent years. The method allows simulation of structures by representing critical components with physically tested specimens and the rest of the structure with numerical models. However, the number of physical specimens is limited by available experimental equipment. Hence, the benefit of the hybrid simulation diminishes when only a few components in a large system can be realistically represented. The objective of the paper is to overcome the limitation through a novel model updating method. The model updating is carried out by applying calibrated weighting factors at each time step to the alternative numerical models, which encompasses the possible variation in the experimental specimen properties. The concept is proposed and implemented in the hybrid simulation framework, UI‐SimCor. Numerical verification is carried out using two‐DOF systems. The method is also applied to an experimental testing, which proves the concept of the proposed model updating method. Copyright © 2013 John Wiley & Sons, Ltd.     

Real-time hybrid simulation for structural control performance assessment

Real-time hybrid simulation is an attractive method to evaluate the response of structures under earthquake loads.The method is a variation of the pseudodynamic testing technique in which the experiment is executed in real time,thus allowing investigation of structural systems with rate-dependent components.Real-time hybrid simulation is challenging because it requires performance of all calculations,application of displacements,and acquisition of measured forces,within a very small increment of time.Furthe...     

Online numerical simulation: A hybrid simulation method for incomplete boundary conditions

Hybrid simulation is a powerful and cost‐effective simulation technique to evaluate structural dynamic performance. However, it is sometimes rather difficult to guarantee all the boundaries on the physical substructures, especially when the boundary conditions are very complex, due to limited laboratory resources. Lacking of boundary conditions is bound to change the stress state of the structure and eventually result in an inaccurate evaluation of structural performance. A model updating‐based online numerical simulation method is proposed in this paper to tackle the problem of incomplete boundary conditions. In the proposed method, 2 sets of finite element models with the same constitutive model are set up for the overall analysis of the whole structure and the constitutive model parameter estimation of the physical substructure, respectively. The boundary conditions are naturally satisfied because the response is calculated from the overall structural model, and the accuracy is improved as the material constitutive parameters are updated. The effectiveness of the proposed method is validated via numerical simulations and actual hybrid tests on a RC frame structure, and the results show that the negative effect of incomplete boundary conditions is almost eliminated and the accuracy of hybrid simulation is very much improved.     

Compensation of actuator delay and dynamics for real‐time hybrid structural simulation

Compensation of delay and dynamic response of servo‐hydraulic actuators is critical for stability and accuracy of hybrid experimental and numerical simulations of seismic response of structures. In this study, current procedures for compensation of actuator delay are examined and improved procedures are proposed to minimize experimental errors. The new procedures require little or no a priori information about the behavior of the test specimen or the input excitation. First, a simple approach is introduced for rapid online estimation of system delay and actuator command gain, thus capturing the variability of system response through a simulation. Second, an extrapolation procedure for delay compensation, based on the same kinematics equations used in numerical integration procedures is examined. Simulations using the proposed procedures indicate a reduction in high‐frequency noise in force measurements that can minimize the excitation of high‐frequency modes. To further verify the effectiveness of the compensation procedures, the artificial energy added to a hybrid simulation as a result of actuator tracking errors is measured and used for demonstrating the improved accuracy in the simulations. Copyright © 2007 John Wiley & Sons, Ltd.     

A computational finite‐element program for hybrid simulation

The essence of real time hybrid simulation (RTHS) is the reliance on a physical test (virtual finite element) in support of a numerical simulation, which is unable to properly simulate it numerically. Hence, the computational support for a hybrid simulation is of paramount importance, and one with anything less than a state of the art computational support may defeat the purpose of such an endeavor. A critical, yet often ignored, component of RTHS is precisely the computational engine, which unfortunately has been a bottleneck for realistic studies. Most researches have focused on either the control or on the communication (mostly in distributed, non‐real time hybrid simulation) leaving the third leg of RTHS (computation) ignored and limited to the simulation of simple models (small number of degrees of freedom and limited nonlinearities). This paper details the development of a specialized software written explicitly to perform, single site, hybrid simulation ranging from pseudo‐dynamic to hard real time ones. Solution strategy, implementation details, and actual applications are reported. Copyright © 2011 John Wiley & Sons, Ltd.     

Towards error‐free hybrid simulation using mixed variables

Two procedures are developed and implemented in a hybrid simulation system (HSS) with the aim of enhancing the accuracy and reliability of the online, i.e. pseudo‐dynamic, test results. The first procedure aims at correcting the experimental systematic error in executing the displacement command signal. The error is calculated as the difference between command and feedback signals and correlated to the actuator velocity using the least‐squares method. A feed‐forward error compensation scheme is devised leading to a more accurate execution of the test. The second procedure employs mixed variables with mode switching between displacement and force controls. The newly derived force control algorithm is evaluated using a parametric study to assess its stability and accuracy. The implementation of the mixed variables procedure is designed to adopt force control for high stiffness states of the structural response and displacement control otherwise, where the resolution of the involved instruments may favour this type of mixed control. A simple pseudo‐dynamic experiment of steel cantilever members is used to validate the HSS. Moreover, two experiments as application examples for the two developed procedures are presented. The two experiments focus on the seismic response of (a) timber shear walls and (b) reinforced concrete frames with and without unreinforced masonry infill wall. Copyright © 2007 John Wiley & Sons, Ltd.     

Implementation of online model updating in hybrid simulation

Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated earthquake loading. Structural system level response can be obtained by expressing the equation of motion for the combined experimental and numerical substructures, and solved using time‐stepping integration similar to pure numerical simulations. It is often assumed that a reliable model exists for the numerical substructures while the experimental substructures correspond to parts of the structure that are difficult to model. A wealth of data becomes available during the simulation from the measured experiment response that can be used to improve upon the numerical models, particularly if a component with similar structural configuration and material properties is being tested and subjected to a comparable load pattern. To take advantage of experimental measurements, a new hybrid test framework is proposed with an updating scheme to update the initial modeling parameters of the numerical model based on the instantaneously‐measured response of the experimental substructures as the test progresses. Numerical simulations are first conducted to evaluate key algorithms for the selection and calibration of modeling parameters that can be updated. The framework is then expanded to conduct actual hybrid simulations of a structural frame model including a physical substructure in the laboratory and a numerical substructure that is updated during the tests. The effectiveness of the proposed framework is demonstrated for a simple frame structure but is extendable to more complex structural behavior and models. Copyright © 2013 John Wiley & Sons, Ltd.     

一种新型混合控制技术的振动台模型试验研究

本文提出了基底隔震和上部结构变刚度／阻尼半主动控制结合的一种新型混合控制型式,并且通过小型电磁振动台模型试验来研究其控制效能,为其今后更进一步理论和实验研究奠定基础。     

Innovative substructuring technique for hybrid simulation of multistory buildings through collapse

Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated dynamic earthquake loads. Particularly for experimental seismic collapse simulation of structures, hybrid testing can be an attractive alternative to earthquake simulators due to the limited capacity of most facilities and the difficulties and risks associated with a collapsing structure on a shaking table. The benefits of hybrid simulation through collapse can be further enhanced through accurate and practical substructuring techniques that do not require testing the entire structure. An innovative substructuring technique for hybrid simulation of structures subjected to large deformations is proposed to simplify the boundary conditions by overlapping the domains between the numerical and experimental subassemblies. The advantages of this substructuring technique are the following: it requires only critical components of the structure to be tested experimentally; it reduces the number of actuators at the interface of the experimental subassemblies; and it can be implemented using typically available equipment in laboratories. Compared with previous overlapping methods that have been applied in hybrid simulation, this approach requires additional sensing in the hybrid simulation feedback loop to obtain internal member forces, but provides significantly better accuracy in the highly nonlinear range. The proposed substructuring technique is verified numerically and validated experimentally, using the response of a four‐story moment‐resisting frame that was previously tested to collapse on an earthquake simulator. Copyright © 2014 John Wiley & Sons, Ltd.     

Theory and implementation of switch‐based hybrid simulation technology for earthquake engineering applications

Hybrid simulation (HS) is a novel technique to combine analytical and experimental sub‐assemblies to examine the dynamic responses of a structure during an earthquake shaking. Traditionally, HS uses displacement‐based control where the finite element program calculates trial displacements and applies them to both the analytical and experimental sub‐assemblies. Displacement‐based HS (DHS) has been proven to work well for most structural sub‐assemblies. However, for specimens with high stiffness, traditional DHS does not work because it is difficult to precisely control hydraulic actuators in small displacement. A small control error in displacement will result in large force response fluctuations for stiff specimens. This paper resolves this challenge by proposing a force‐based HS (FHS) algorithm that directly calculates trial forces instead of trial displacements. The proposed FHS is finite element based and applicable to both linear and nonlinear systems. For specimens with drastic changes in stiffness, such as yielding, a switch‐based HS (SHS) algorithm is proposed. A stiffness‐based switching criterion between the DHS and FHS algorithms is presented in this paper. All the developed algorithms are applied to a simple one‐story one‐bay concentrically braced moment frame. The result shows that SHS outperforms DHS and FHS. SHS is then utilized to validate the seismic performance of an innovative earthquake resilient fused structure. The result shows that SHS works in switching between the DHS and FHS modes for a highly nonlinear and highly indeterminate structural system. Copyright © 2017 John Wiley & Sons, Ltd.     

Stability and accuracy in a hybrid test example

This paper presents an example of the application of error monitoring techniques to the results of a pseudodynamic test performed at variable testing speeds. For the faster testing speeds, the control errors increased and the test reliability was lost in terms of accuracy and stability, as observed by the evolution of the monitoring parameters. The applied monitoring methods were the spatial model identification of frequency and damping distortions and the error energy, which have been proposed in previous publications. Copyright © 2012 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.     

Combined implicit or explicit integration steps for hybrid simulation

Explicit integration procedures have been widely adapted and applied to hybrid simulations of the seismic response of structures due to their simplicity. However, these procedures are only conditionally stable and have limited recent applications of hybrid simulations to simple structural models with few degrees of freedom. A novel integration procedure is proposed herein, in which a fully implicit formulation is applied to solve the equation of motion for the hybrid model, but defaults to an explicit or noniterative formulation in steps that fail to converge. The advantages to this approach are the ensured continuity of the simulation and the reduced accumulation of errors that occur during consecutive explicit steps that may lead to instability. The implicit procedure is applied by loading the experimental substructures beyond the expected displacement for the current step, then using the displacements and forces measured through the load path in the iterative implicit scheme. This approach captures the instantaneous behaviour of experimental substructures without physically imposing iterations. Numerical and experimental simulations demonstrate the effectiveness of the proposed integration scheme for multi‐degree‐of‐freedom models, especially in utilization of longer time steps that exceed stability limits of explicit methods, prevention of excitation of higher modes, and testing of stiff systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of implicit HHT‐α integration algorithm for real‐time hybrid simulation

Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd.