Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

Model-based framework for multi-axial real-time hybrid simulation testing

Real-time hybrid simulation is an efficient and cost-effective dynamic testing technique for performance evaluation of structural systems subjected to earthquake loading with rate-dependent behavior. A loading assembly with multiple actuators is required to impose realistic boundary conditions on physical specimens. However, such a testing system is expected to exhibit significant dynamic coupling of the actuators and suffer from time lags that are associated with the dynamics of the servo-hydraulic system, as well as control-structure interaction （CSI）. One approach to reducing experimental errors considers a multi-input, multi-output （MIMO） controller design, yielding accurate reference tracking and noise rejection. In this paper, a framework for multi-axial real-time hybrid simulation （maRTHS） testing is presented. The methodology employs a real-time feedback-feedforward controller for multiple actuators commanded in Cartesian coordinates. Kinematic transformations between actuator space and Cartesian space are derived for all six-degrees-of- freedom of the moving platform. Then, a frequency domain identification technique is used to develop an accurate MIMO transfer function of the system. Further, a Cartesian-domain model-based feedforward-feedback controller is implemented for time lag compensation and to increase the robustness of the reference tracking for given model uncertainty. The framework is implemented using the 1/5th-scale Load and Boundary Condition Box （LBCB） located at the University of Illinois at Urbana- Champaign. To demonstrate the efficacy of the proposed methodology, a single-story frame subjected to earthquake loading is tested. One of the columns in the fraane is represented physically in the laboratory as a cantilevered steel column. For real- time execution, the numerical substructure, kinematic transformations, and controllers are implemented on a digital signal processor. Results show excellent performance of the maRTHS framework when six-degrees-of-freedom are controUed at the interface between substructures.

Real-Time Hybrid Simulation of Seismically Isolated Structures with Full-Scale Bearings and Large Computational Models

Hybrid simulation can be a cost effective approach for dynamic testing of structural components at full scale while capturing the system level response through interactions with a numerical model.The dynamic response of a seismically isolated structure depends on the combined characteristics of the ground motion,bearings,and superstructure.Therefore,dynamic full-scale system level tests of isolated structures under realistic dynamic loading conditions are desirable towards a holistic validation of this earthquake protection strategy.Moreover,bearing properties and their ultimate behavior have been shown to be highly dependent on rate-of-loading and scale size effects,especially under extreme loading conditions.Few laboratory facilities can test full-scale seismic isolation bearings under prescribed displacement and/or loading protocols.The adaptation of a full-scale bearing test machine for the implementation of real-time hybrid simulation is presented here with a focus on the challenges encountered in attaining reliable simulation results for large scale dynamic tests.These advanced real-time hybrid simulations of large and complex hybrid models with several thousands of degrees of freedom are some of the first to use high performance parallel computing to rapidly execute the numerical analyses.Challenges in the experimental setup included measured forces contaminated by delay and other systematic control errors in applying desired displacements.Friction and inertial forces generated by the large-scale loading apparatus can affect the accuracy of measured force feedbacks.Reliable results from real-time hybrid simulation requires implementation of compensation algorithms and correction of these various sources of errors.Overall,this research program confirms that real-time hybrid simulation is a viable testing method to experimentally assess the behavior of full-scale isolators while capturing interactions with the numerical models of the superstructure to evaluate system level and in-structure response.

Control performance comparison between tuned liquid damper and tuned liquid column damper using real-time hybrid simulation

Tuned liquid damper (TLD) and tuned liquid column damper (TLCD) are two types of passive control devices that are widely used in structural control. In this study, a real-time hybrid simulation (RTHS) technique is employed to investigate the diff erence in control performance between TLD and TLCD. A series of RTHSs is presented with the premise of the same liquid length, mass ratio, and structural parameters. Herein, TLD and TLCD are physically experimented, and controlled structures are numerically simulated. Then, parametric studies are performed to further evaluate the diff erent performance between TLD and TLCD. Experimental results demonstrate that TLD is more eff ective than TLCD under diff erent amplitude excitations.

Analysis of actuator delay and its effect on uncertainty quantification for real-time hybrid simulation

Uncertainties in structure properties can result in different responses in hybrid simulations. Quantification of the effect of these tmcertainties would enable researchers to estimate the variances of structural responses observed from experiments. This poses challenges for real-time hybrid simulation （RTHS） due to the existence of actuator delay. Polynomial chaos expansion （PCE） projects the model outputs on a basis of orthogonal stochastic polynomials to account for influences of model uncertainties. In this paper, PCE is utilized to evaluate effect of actuator delay on the maximum displacement from real-time hybrid simulation of a single degree of freedom （SDOF） structure when accounting for uncertainties in structural properties. The PCE is first applied for RTHS without delay to determine the order of PCE, the number of sample points as well as the method for coefficients calculation. The PCE is then applied to RTHS with actuator delay. The mean, variance and Sobol indices are compared and discussed to evaluate the effects of actuator delay on uncertainty quantification for RTHS. Results show that the mean and the variance of the maximum displacement increase linearly and exponentially with respect to actuator delay, respectively. Sensitivity analysis through Sobol indices also indicates the influence of the single random variable decreases while the coupling effect increases with the increase of actuator delay.

Restoring force correction based on online discrete tangent stiffness estimation method for real-time hybrid simulation

In real-time hybrid simulation（RTHS）, it is difficult if not impossible to completely erase the error in restoring force due to actuator response delay using existing displacement-based compensation methods. This paper proposes a new force correction method based on online discrete tangent stiffness estimation（online DTSE） to provide accurate online estimation of the instantaneous stiffness of the physical substructure. Following the discrete curve parameter recognition theory, the online DTSE method estimates the instantaneous stiffness mainly through adaptively building a fuzzy segment with the latest measurements, constructing several strict bounding lines of the segment and calculating the slope of the strict bounding lines, which significantly improves the calculation efficiency and accuracy for the instantaneous stiffness estimation. The results of both computational simulation and real-time hybrid simulation show that：（1） the online DTSE method has high calculation efficiency, of which the relatively short computation time will not interrupt RTHS; and（2） the online DTSE method provides better estimation for the instantaneous stiffness, compared with other existing estimation methods. Due to the quick and accurate estimation of instantaneous stiffness, the online DTSE method therefore provides a promising technique to correct restoring forces in RTHS.

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. Furthermore, unless appropriate compensation for actuator dynamics is implemented, stability problems are likely to occur during the experiment. This paper presents an approach for real-time hybrid simulation in which compensation for actuator dynamics is implemented using a model-based feedforward compensator. The method is used to evaluate the response of a semi-active control of a structure employing an MR damper. Experimental results show good agreement with the predicted responses, demonstrating the effectiveness of the method for structural control performance assessment.

Real-time hybrid simulation of structures equipped with viscoelastic-plastic dampers using a user-programmable computational platform

A user-programmable computational/control platform was developed at the University of Toronto that offers real-time hybrid simulation （RTHS） capabilities. The platform was verified previously using several linear physical substructures. The study presented in this paper is focused on further validating the RTHS platform using a nonlinear viscoelastic-plastic damper that has displacement, frequency and temperature-dependent properties. The validation study includes damper component characterization tests, as well as RTHS of a series of single-degree-of-freedom （SDOF） systems equipped with viscoelastic-plastic dampers that represent different structural designs. From the component characterization tests, it was found that for a wide range of excitation frequencies and friction slip loads, the tracking errors are comparable to the errors in RTHS of linear spring systems. The hybrid SDOF results are compared to an independently validated thermal- mechanical viscoelastic model to further validate the ability for the platform to test nonlinear systems. After the validation, as an application study, nonlinear SDOF hybrid tests were used to develop performance spectra to predict the response of structures equipped with damping systems that are more challenging to model analytically. The use of the experimental performance spectra is illustrated by comparing the predicted response to the hybrid test response of 2DOF systems equipped with viscoelastic-plastic dampers.

Comparison of delay compensation methods for real-time hybrid simulation using frequency-domain evaluation index

The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

Theoretical and experimental studies on critical time delay of multi-DOF real-time hybrid simulation

This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discrete-time root locus(RL)techniques,respectively.A bilinear transform is introduced into the first-order Padéapproximation while conducting the discrete RL analysis.Based on this technique,the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be analyzed.Subsequently,the critical time delays calculated by the continuous-and discrete-time RL techniques,respectively,are compared for a 2-DOF RTHS system.It is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time delay.Finally,theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS experiments.Parametric analysis provides a glimpse of the effects of time step,frequency and damping ratio in a performing partitioning scheme.The constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance,therefore facilitating successful RTHS.

Seismic performance evaluation of VCFPB isolated storage tank using real-time hybrid simulation

Variable curvature friction pendulum bearings(VCFPB)effectively reduce the dynamic response of storage tanks induced by earthquakes.Shaking table testing is used to assess the seismic performance of VCFPB isolated storage tanks.However,the vertical pressure and friction coefficient of the scaled VCFPB in the shaking table tests cannot match the equivalent values of these parameters in the prototype.To avoid this drawback,a real-time hybrid simulation(RTHS)test was developed.Using RTHS testing,a 1/8 scaled tank isolated by VCFPB was tested.The experimental results showed that the displacement dynamic magnification factor of VCFPB,peak reduction factors of the acceleration,shear force,and overturning moment at bottom of the tank,were negative exponential functions of the ratio of peak ground acceleration(PGA)and friction coefficient.The peak reduction factors of displacement,acceleration,force and overturning moment,which were obtained from the experimental results,are compared with those calculated by the Housner model.It can be concluded that the Housner model is applicable in estimation of the acceleration,shear force,and overturning moment of liquid storage tank,but not for the sliding displacement of VCFPBs.

Seismic performance of steel MRF building with nonlinear viscous dampers

This paper presents an experimental study of the seismic response of a 0.6-scale three-story seismicresistant building structure consisting of a moment resisting frame （MRF） with reduced beam sections （RBS）, and a frame with nonlinear viscous dampers and associated bracing （called the DBF）. The emphasis is on assessing the seismic performance for the design basis earthquake （DBE） and maximum considered earthquake （MCE）. Three MRF designs were studied, with the MRF designed for 100%, 75%, and 60%, respectively, of the required base shear design strength determined according to ASCE 7-10. The DBF with nonlinear viscous dampers was designed to control the lateral drift demands. Earthquake simulations using ensembles of DBE and MCE ground motions were conducted using the real-time hybrid simulation method. The results show the drift demand and damage that occurs in the MRF under seismic loading. Overall, the results show that a high level of seismic performance can be achieved under DBE and MCE ground motions, even for a building structure designed for as little as 60% of the base shear design strength required by ASCE 7-10 for a structure without dampers.