Error Influence Analysis And Correction Methods For Real-time Hybrid Simulation

Real time hybrid simulation(RTHS)is a novel dynamic test method with the capability of computing,dynamic loading and information communication in high speed.Using the substructure test principle,RTHS divides a structural system into the numerical and physical substructures,where the former is analytically modeled through a finite element program and the latter is physically tested in laboratories.The method significantly reduces the experiment expense and provides the most advanced solution for large-scale structures with rate-dependent behavior in size limited laboratories,which is regarded as the development direction of civil engineering experiments in the future.Currently,RTHS is in rapid development,this paper aims at solving the key techniques of error influence analysis and correction method in RTHS through theoretical analysis,numerical simulation and experimental verification.The main contents of this paper are as follows:1.Effect of actuator delay on RTHS system stabilityAccording to the RTHS results on a spring,it is demonstrated that the actuator response delay is more consistent with the time-varying delay assumption,while the assumption of constant actuator delay helps simplify the stability analysis of RTHS.In order to study the effect of time-varying delay/constant delay on system stability,this paper adopts the Lyapunov-Krasovskii(L-K)stability theory and proposes the stability criteria for the single-degree-offreedom(SDOF)with single time delay and the multiple-degree-of-freedom(MDOF)with multiple time delay system in the form of matrix inequality.Due to the L-K stability theorem is conservative,the proposed criteria are sufficient but unnecessary conditions for the stability of time delay system.This study further demonstrates that,(1)the stable region of time-varying delay system shrinks with the increase of the first derivative of timevarying delay;(2)the stable region of time-varying delay system is always smaller than that of constant time delay system.The above conclusions overturn that the time-varying delay and the constant time delay have the same effect on the stability of system.It is proved that the constant time delay simplification of the actuator response delay expands the true stability region of the system.Computational simulations for RTHS of a linear SDOF system with time-varying actuator delay further show that the stable region of time-varying delay system is only significantly affected by time-varying delay when the stiffness ratio for physical substructure is smaller than 0.2 and the natural period of prototype structure is larger than 1.5Hz.While for other linear SDOF scenarios,the influence of timevarying delay can be ignored and analysis based on assumption of constant time delay is applicable.Additionally,with the increase of the number of degrees-of-freedom(DOFs)of system and the sources of actuator delay,the accuracy of L-K stability criterion decreases slowly,meanwhile the negative effect of time-varying delays on the stability of system rises gradually.2.Restoring force correction method based on discrete tangent stiffness estimationRTHS requires extremely high synchronicity of testing equipment,the actuator displacement tracking error,including undershooting and overshooting,will cause energy dissipation/accumulation in test system.The most important variable in the restoring force correction method is the instantaneous stiffness of the test specimen.The traditional methods usually use a fixed length historical data to calculate the instantaneous stiffness of test specimen,which may contains a large amount of outdated information.The outdated historical data poses a serious hazard to the estimation of the instantaneous stiffness of the test specimen.Based on the geometrical analysis approach and the theory of discrete curve parameter recognition,this study develops an online discrete tangent stiffness estimation(Online DTSE)method for RTHS.For different magnitudes of measurement noise,the method can adaptively select and retain a series of latest valid data and ignore outdated information,then constructs the tangent of the discrete displacement-restoring force curve according to the squeeze principle,of which the advantage is highly improving the accuracy and promptness of instantaneous stiffness estimation.Both computational simulation and real-time test results verified the accuracy and effectiveness of this method.Compared to the displacement compensation method alone,the combined utilization of displacement compensation and restoring force correction method can significantly reduce the energy accumulation error 60-80% in the test and obtain more an accurate test result.3.Influence of calculation delay and full simulation software developmentThis study completed a sliding bearing RTHS by using the testing scheme provided by MTS Corporation.The result shows that the computational delay occurs in the experiment at some time steps.The main reason for this phenomenon is that OpenSees automatically selects the Generalized-α implicit integration algorithm with the characteristic of excellent accuracy and stability but low computational efficiency and long time-consuming.RTHS requires extremely high synchronization of the test,while the appearance of computational delay is contingent and random,which cannot be fully predicted and compensated,hence the computational delay causes serious damage of the continuity and real time performance of the test.In order to overcome the computational delay and to take the time delay effect of actuator into account,this paper develops a full simulation of real-time hybrid test(FSRTHT)software based on MATLAB/GUI environment.The software has a visual interface,and the human-computer interaction is friendly.Moreover,the test process is simplified and explicit integration algorithm is added in the software.Hence,the FSRTHT software can simulate the whole process of the test,including conduct pre-simulation analysis before the test,control process of the test and analyze the experiment results after the test.4.Real-time hybrid simulation of base isolator systemIn order to verify and promote the real-time hybrid simulation,this study selects a sliding isolator/lead rubber bearing as a physical substructure,and develops the mechanical properties of isolator/bearing and the isolation effect of the integral structure under real seismic excitation.The test result of sliding isolator shows that the friction coefficient of the sliding isolator is related to the loading frequency and vertical pressure;the friction bearing element has good performance in reflecting the friction property and energy dissipation of the sliding isolator;the isolated structure using the sliding isolator can lead to the superstructure slide through the horizontal deformation of the isolation layer,which consumes the seismic energy and reduces the damage.The lead rubber bearing test is pre-simulated by using FSRTHT,including analyzing the influence of the actuator delay,examining the compensation and correction method,estimating the peak of the displacement and restoring force.During the test,FSRTHT controls the process by using Simulink.After the test,FSRTHT automatically analyzes and evaluates the experiment results.The bearing test shows that the combined use of displacement compensation method and force correction method can significantly reduce the loading error of actuator;lead rubber bearing can reduce the earthquake hazard by increasing the structural natural vibration period and energy consumption for deformation.