Real-time Substructure Testing Research Articles

Shaking Tables Test on Seismic Responses of a Long-Span Rigid-Framed Bridge Considering Traveling Wave Effect and Soil–Structure Interaction

The traveling wave effect and soil–structure interaction have significant influence on the seismic response of large-span bridges with complex site conditions. In this paper, a 1/10 scaled-down large-span rigid-framed bridge model was designed and fabricated, and a shaking tables test considering the traveling wave effect and soil–structure interaction was carried out on a large-scale continuous rigid bridge model by a real-time substructure hybrid test technique. Influences of the traveling wave effect and soil–structure interaction on the seismic responses of the rigid-framed bridge specimen were systematically analyzed with experimental data. The test results showed that when the apparent wave speed was small, the traveling wave effect increased the seismic responses of the rigid-framed bridge. With the increase in apparent wave speed, the structural response under traveling wave excitation and uniform excitation was basically the same. The SSI effect lead to a great change in the seismic input peaks and spectral characters at the bottom of the pier, and increased the seismic responses of the rigid-framed bridge. When both traveling wave and the SSI effect were considered, there was a phase difference in the seismic excitation. The dynamic responses of a continuous rigid-framed bridge could not be simply obtained by superposition of the separate traveling wave effect or SSI effect. Meanwhile, the real-time substructure test method in this paper solved the problems that the traditional soil box experiment cannot be applied to the test of a large-scale model, the soil and bridge structure find it difficult to meet the unified similarity ratio, and the boundary conditions are difficult to simulate accurately.

Improved Operator-Splitting Method for Dynamic Real-Time Substructure Testing of Multiple-Degree-of-Freedom Structure

The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering.

Applications of the RST Algorithm to Nonlinear Systems in Real-Time Hybrid Simulation

Real-time substructure testing (RST) algorithm is a newly developed integration method for real-time hybrid simulation (RTHS) which has structure-dependent and explicit formulations for both displacement and velocity. The most favourable characteristics of the RST algorithm is unconditionally stable for linear and no iterations are needed. In order to fully evaluate the performance of the RST method in solving dynamic problems for nonlinear systems, stability, numerical dispersion, energy dissipation, and overshooting properties are discussed. Stability analysis shows that the RST method is only conditionally stable when applied to nonlinear systems. The upper stability limit increases for stiffness-softening systems with an increasing value of the instantaneous degree of nonlinearity while decreases for stiffness-hardening systems when the instantaneous degree of nonlinearity becomes larger. Meanwhile, the initial damping ratio of the system has a negative impact on the upper stability limit especially for instantaneous stiffness softening systems, and a larger value of the damping ratio will significantly decrease the upper stability limit of the RST method. It is shown in the accuracy analysis that the RST method has relatively smaller period errors and numerical damping ratios for nonlinear systems when compared with other two well-developed algorithms. Three simplified engineering cases are presented to investigate the dynamic performance of the RST method, and the numerical results indicate that this method has a more desirable accuracy than other methods in solving dynamic problems for both linear and nonliner systems.

Real-Time Substructure Tests and Numerical Simulation of Mechanical Characteristics of Natural Rubber-Laminated Bearings

Natural rubber lamination is a kind of seismic isolation of bearings often used in civil engineering. The advantage of laminated bearings is large vertical stiffness and small lateral stiffness. In seismic regions, structural periods would be extended and the effect of seismic forces can be lowered using bearings. In previous tests, the static cyclic loading method was mainly used that failed to take account of the loading rate. The real-time substructure testing is proposed to simulate true seismic loads. This testing and test setup were first introduced, and the effect of the loading rate was studied. Then the effects of vertical pressure and peak acceleration of ground motion were studied. At last the test results were simulated by the finite element method, and an accurate method to calculate seismic responses of bridges with laminated bearings was proposed.

Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement (V+D)-based equivalent force control (EFC) method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological (MR) damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.

A dynamic load estimation method for nonlinear structures with unscented Kalman filter

Abstract A force estimation method is proposed for hysteretic nonlinear structures. The equation of motion for the nonlinear structure is represented in state space and the state variable is augmented by the unknown the time history of external force. Unscented Kalman filter (UKF) is improved for the force identification in state space considering the ill-condition characteristic in the computation of square roots for the covariance matrix. The proposed method is firstly validated by a numerical simulation study of a 3-storey nonlinear hysteretic frame excited by periodic force. Each storey is supposed to follow a nonlinear hysteretic model. The external force is identified and the measurement noise is considered in this case. Then a case of a seismically isolated building subjected to earthquake excitation and impact force is studied. The isolation layer performs nonlinearly during the earthquake excitation. Impact force between the seismically isolated structure and the retaining wall is estimated with the proposed method. Uncertainties such as measurement noise, model error in storey stiffness and unexpected environmental disturbances are considered. A real-time substructure testing of an isolated structure is conducted to verify the proposed method. In the experimental study, the linear main structure is taken as numerical substructure while the one of the isolations with additional mass is taken as the nonlinear physical substructure. The force applied by the actuator on the physical substructure is identified and compared with the measured value from the force transducer. The method proposed in this paper is also validated by shaking table test of a seismically isolated steel frame. The acceleration of the ground motion as the unknowns is identified by the proposed method. Results from both numerical simulation and experimental studies indicate that the UKF based force identification method can be used to identify external excitations effectively for the nonlinear structure with accurate results even with measurement noise, model error and environmental disturbances.

Thermodynamic analysis of temperature shrinkage effect of wall filled frame structure

The existence of temperature cracks seriously affects the use of infilled walls. This paper reports on the analysis of finite element numerical simulation about this. The calculation method of wall temperature stress had been discussed, and found the determining method for location of temperature crack. And on this basis, it studied on the wall crack design theory based on temperature effect. Though the real-time substructure test, research the main factors of temperature shrinkage that affect wall cracking. It was found that the temperature contraction developed rapidly in the early stage, and then slowed down gradually, after 28 days, the shrinkage of each specimen was almost stable. Compared with the standard curing condition, the temperature shrinkage was more obvious under natural curing condition. Also the cement mortar shrinkage effect is better than that of mixed mortar in reducing temperature shrinkage. These conclusions provide a reference for controlling the cracking of wall.

Effect of Soil-Structure Interaction on Seismic Performance of Long-Span Bridge Tested by Dynamic Substructuring Method

Because of the limitations of testing facilities and techniques, the seismic performance of soil-structure interaction (SSI) system can only be tested in a quite small scale model in laboratory. Especially for long-span bridge, a smaller tested model is required when SSI phenomenon is considered in the physical test. The scale effect resulting from the small scale model is always coupled with the dynamic performance, so that the seismic performance of bridge considering SSI effect cannot be uncovered accurately by the traditional testing method. This paper presented the implementation of real-time dynamic substructuring (RTDS), involving the combined use of shake table array and computational engines for the seismic simulation of SSI. In RTDS system, the bridge with soil-foundation system is divided into physical and numerical substructures, in which the bridge is seen as physical substructures and the remaining part is seen as numerical substructures. The interface response between the physical and numerical substructures is imposed by shake table and resulting reaction force is fed back to the computational engine. The unique aspect of the method is to simulate the SSI systems subjected to multisupport excitation in terms of a larger physical model. The substructuring strategy and the control performance associated with the real-time substructuring testing for SSI were performed. And the influence of SSI on a long-span bridge was tested by this novel testing method.

Applications of a Family of Unconditionally Stable, Dissipative, Explicit Methods to Pseudodynamic Tests

A newly developed dissipative family method is adopted and implemented for pseudodynamic tests in this investigation since it can have desired numerical properties. In fact, it can integrate unconditional stability, second-order accuracy and favorable numerical dissipation together. In addition, its pseudo-dynamic implementation involves no iteration procedure for each time step due to the explicitness of each time step. Hence, this pseudodynamic algorithm is promising for solving an inertial problem, where the total response is dominated by low frequency modes and the high frequency responses are of no interest. Currently, there is no pseudodynamic algorithm can have such desired numerical properties for practical applications. In addition to the application to a general pseudodynamic test, it might enable the ability to conduct a real-time substructure test for a large degree of freedom system due to its computational efficiency.

Sliding mode for equivalent force control in real-time substructure testing

SUMMARY The equivalent force control method uses feedback control to replace a mathematical iteration to solve the nonlinear difference equation in a real-time substructure test with an implicit integration method. The commonly used PID controller as a candidate of equivalent force control has only limited robustness for nonlinear systems. For real-time substructure testing with nonlinear specimens, the sliding mode control is proposed as the outer-loop controller of the equivalent force control. The design approach and implementation issues are discussed analytically. The effects of key parameters of sliding mode controller on the performance of equivalent force control are demonstrated through numerical simulation. The real-time as well as pseudodynamic substructure tests are carried out with a linear elastic spring and a nonlinear buckling restrained brace as experimental substructures. The effectiveness of the sliding mode control is verified by these tests. Copyright © 2014 John Wiley & Sons, Ltd.

Improved model for real-time substructuring testing system

Real-time substructuring (RTS) is a hybrid technique meant for evaluation of dynamic response of large structures. The critical component of the structure is experimentally tested, while the remaining components are modelled numerically. This paper discusses about various issues associated with the simulation of RTS. An improved model based on Simulink module of MATLAB is proposed to create the actual experimental conditions. Detailed model of electro servohydraulic actuator based on fluid power engineering is used to emulate the nonlinear behaviour of the actuator. As the response of the actuator is a function of specimen, the actuator model involves boundary conditions of the experimental setup. Such detailed model is then simplified to develop a transfer function for the actuator. Feedforward compensator with modified inverse dynamics is employed to compensate for actuator dynamics. Time integration is carried out by using Rosenbrock-W method, to solve the dynamic equations of motion of the numerical substructure. The dynamic response of a linear single degree of freedom (SDOF) system, nonlinear SDOF system and linear multi degree of freedom (MDOF) system to El-Centro earthquake is evaluated by using the proposed RTS model. The evaluated responses are compared with those obtained from the numerical analysis of full structure without substructuring using Operator Splitting Method (OSM). Upon comparison, the proposed model is found to be suitable for evaluation of the dynamic response of a structure.

Performance and Application of Equivalent Force Control Method for Real-Time Substructure Testing

AbstractThe equivalent force control (EFC) method has been developed for real-time substructure testing with implicit integration to replace the numerical iterative process with feedback control. This paper addresses two issues concerning the performance of this method. One is the determination of the force-displacement conversion factor (a key component of EFC) for nonlinear specimens. The analysis conducted here shows that the force-displacement conversion factor is largely governed by the properties of the numerical substructure and the numerical scheme when a small integration time interval is used. Otherwise, the factor has to be determined with the secant stiffness of the specimen and of the numerical substructure if a proportional-derivative controller is used for EFC. The other issue is the overshooting problem, which may arise for multidegree-of-freedom structures because of the relatively quick response feedback from the numerical substructure in the closed-loop EFC. This problem can be resolved...

Advances beyond transfer system dynamics compensation in real-time dynamic substructuring tests

Real-time dynamic substructuring tests, also known as hybrid tests, are critically affected by the dynamic nature of the actuators used to substitute the numerical substructure. These actuators are widely considered as transfer systems, which transfer magnitudes calculated via simulation of the numerical substructure to the physical substructure. Control engineering efforts in this area have, with few exceptions, traditionally been focused on compensation of the transfer system dynamics, in order to obtain perfect transfer systems. This article shows that the role of control systems in the context of real-time substructuring tests is not limited to transfer system dynamics compensation. Similarly, the role of actuators need not be that of transfer systems. As a result, a novel range of methods opens for actuator and control system design, which presents significant advantages over transfer systems with their corresponding dynamics compensation schemes.

Equivalent Force Control Method for Real-time Testing of Nonlinear Structures

The equivalent force control (EFC) method replaces numerical iteration with a feedback control strategy to solve the nonlinear equations of motion using an implicit integration method for real-time substructure tests (RSTs). The method, however, requires the conversion of the equivalent forces to structural displacements using a conversion matrix. It is demonstrated in this article that with the use of a proportional-integral (PI) controller for the EFC, one has the convenience of choosing the initial stiffness matrix of a structure to construct the conversion matrix regardless of the properties and degree of nonlinearity of the system. The stability condition of the EFC using a PI controller has been derived with the Routh stability criterion. Methods for designing and tuning a PI controller for RST using EFC have been presented and excellent system performance has been obtained from numerical simulations and actual tests. The simulation results showed that the EFC method using a PI controller and the initial stiffness matrix to construct the conversion matrix can deliver excellent performance even for structural systems that develop a severe strain-softening behavior. Its superiority over iteration method proposed by Jung et al. [2007] was demonstrated through numerical simulation. This provides an efficient means to test nonlinear multiple-degrees-of-freedom structures.

Operator‐splitting method for real‐time substructure testing

AbstractIt has been shown that the operator‐splitting method (OSM) provides explicit and unconditionally stable solutions for quasi‐static pseudo‐dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real‐time substructure testing (RST) when the velocity‐dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM‐RST algorithm are investigated. It is shown that the OSM‐RST is unconditionally stable so long as the non‐linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM‐RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non‐classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM‐RST is preserved when the experimental substructure generates velocity‐dependent reaction forces, whereas the stability of real‐time substructure tests based on the central difference method is worsened by the damping of the specimen. Copyright © 2005 John Wiley & Sons, Ltd.

Stability and accuracy analysis of the central difference method for real‐time substructure testing

AbstractThe central difference method (CDM) that is explicit for pseudo‐dynamic testing is also believed to be explicit for real‐time substructure testing (RST). However, to obtain the correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as the displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the required modification of the standard central difference method when applied to RST and analyzes the stability and accuracy of the modified CDM for RST. Copyright © 2005 John Wiley & Sons, Ltd.

Stability and Delay Compensation for Real-Time Substructure Testing

Real-time substructure testing is a method for establishing the dynamic behavior of structural systems. The method separates a complex structure into physical and numerically modeled substructures, which interact in real-time allowing time-dependent nonlinear behavior of the physical specimen to be accurately represented. Displacements are applied to the physical specimen using hydraulic actuators and the resulting measured forces are fed back to the numerical substructure. This feedback loop is implemented as a time-stepping routine. One of the key factors in obtaining reliable results using this method is the accurate compensation of the delayed response of the actuator. If this is not accounted for, instability of the feedback loop is likely to occur. This paper presents a method for estimating the delay while a test is in progress and accurately compensating for it during the test. The stability of both linear and nonlinear single-actuator systems is examined and the behavior of twin-actuator systems ...

The development of real–time substructure testing

Full-scale dynamic testing of civil engineering structures is extremely costly and difficult to perform. Most test methods therefore involve either a reduction in the physical scale or an extension of the time-scale. Both of these approaches can cause significant difficulties in extrapolating to the full-scale dynamic behaviour, particularly when the structure responds nonlinearly or includes highly rate-dependent components such as dampers. Real-time substructure testing is a relatively new method which seeks to avoid these problems by performing tests on key elements of the structure at full or large scale, with the physical test coupled in real time to a numerical model of the surrounding structure. The method requires a high performance of both the physical test equipment and the numerical algorithms. This paper first reviews the development of structural test methods and the emergence of real-time substructure testing. This is followed by a brief description of the equipment that is needed to implement a substructure test. Several novel developments in the numerical algorithms used in real-time substructure testing are presented, including a new, fast algorithm which allows nonlinear response of the surrounding structure to be computed in real time. Results are presented from a variety of tests which demonstrate the performance of the system at small and large scale, with either linear or nonlinear test specimens, and with varying numbers of degrees of freedom passed between the physical and numerical substructures. Finally, the usefulness and possible applications of the test method are discussed.

Numerical Modeling of a Servohydraulic Testing System for Structures

A realistic model of a dynamic testing laboratory for structures is presented, which includes the controller and the hydraulic loading equipment as well as the test specimen. The model provides a safe and easily controllable way of experimenting with a complex dynamic testing system, enabling the limits of the system to be explored prior to performing a physical test. The paper describes the representation of the proportional, integral, derivative, lag controller and the development of a detailed nonlinear model of the servovalve actuator system, together with their numerical implementation using the Matlab system-modeling package Simulink. Output from the model is compared with experimental results of both open-loop tests and real-time substructure tests, in which a physical test of part of a structure is coupled in real time to a numerical model of the remainder of the structure.

Improved control algorithm for real‐time substructure testing

AbstractReal‐time substructure testing is a novel method of testing structures under dynamic loading. The complete structure is separated into two substructures, one of which is tested physically at large scale and in real time, so that time‐dependent non‐linear behaviour of the substructure is realistically represented. The second substructure represents the surrounding structure, which is modelled numerically. In the current formulation this numerical substructure is assumed to remain linear. The two substructures interact in real‐time so that the response of the complete structure, incorporating the non‐linear behaviour of the physical substructure, is accurately represented. This paper presents several improvements to the linear numerical modelling of substructures for use in explicit time‐stepping routines for real‐time substructure testing. An extrapolation of a first‐order‐hold discretization is used which increases the accuracy of the numerical model over more direct explicit methods. Additionally, an integral form of the equation of motion is used in order to reduce the effects of noise and to take into account variations of the input over a time‐step. In order to take advantage of this integral form, interpolation of the model output is performed in order to smooth the output. The improvements are demonstrated using a series of substructure tests on a simple portal frame. While the testing approach is suitable for cases in which the physical substructure behaves non‐linearly, the results presented here are for fully linear systems. This enables comparisons to be made with analytical solutions, as well as with the results of tests based on the central difference method. Copyright © 2001 John Wiley & Sons, Ltd.