Numerical Substructure Research Articles

Real-time Hybrid Test on a Semi-actively Controlled Building Structure Equipped with Full-scale MR Dampers

The real-time hybrid testing method (RT-HYTEM) is a structural testing technique in which the numerical integration of the equation of motion for a numerical substructure and the physical testing for an experimental substructure are performed simultaneously in real-time. This article presents the quantitative evaluation of the seismic performance of a building structure installed with a magnetorheological (MR) damper using RT-HYTEM. A building model is identified from the force-vibration testing results of a full-scale five-story building and is used as the numerical substructure, and an MR damper corresponding to an experimental substructure is physically tested using a universal testing machine (UTM). First, the force required to drive the displacement of the story, at which the MR damper is located, is measured from the load cell attached to the UTM. The measured force is then returned to a control computer to calculate the response of the numerical substructure. Finally, the experimental substructure is excited by the UTM with the calculated response of the numerical substructure. The RT-HYTEM implemented in this study is validated because the real-time hybrid testing results obtained by application of sinusoidal and earthquake excitations and the corresponding analytical results obtained using the Bouc-Wen model as the control force of the MR damper with respect to input currents are in good agreement. Also, the results from RT-HYTEM for the passive -on and -off control show that the structural responses did not decrease further by the excessive control force, but decreased due to the increase of the current applied to the MR damper. Also, two semi-active control algorithms (modulated homogeneous friction and the clipped-optimal control algorithms) are applied to the MR damper in order to optimally control the structural responses. To compare the RT-HYTEM and numerical results, Bouc-Wen model parameters are identified for each input current. The results of the comparison of experimental and numerical responses show that it is more practical to use RT-HYTEM in semi-active devices such as MR dampers. The test results show that a control algorithm can be experimentally applied to the MR damper using RT-HYTEM. This article provides a discussion on each algorithm with respect to the seismic performances.

Model predictive control of dynamically substructured systems with application to a servohydraulically actuated mechanical plant

Dynamically substructured systems (DSS) are increasingly used by the dynamics testing community. DSS involves the physical testing of full-size critical components in parallel with numerical testing of the remaining components. This has certain advantages over other testing methods. However, the synchronisation of the signals at the interface between the physical and numerical substructures of DSS requires a high fidelity controller. In practice, the performance of the DSS testing can be degraded by input saturation of the actuators. In this study, the authors use model predictive control (MPC) to cope with the saturation problem in DSS. To facilitate the MPC and observer design for DSS, a modified DSS framework based on an existing one is proposed. As a case study, a quasi-motorcycle (QM) system is converted into the modified DSS framework and a traditional on-line MPC control strategy is implemented in real time.

Testing of dynamically substructured, base‐isolated systems using adaptive control techniques

AbstractExperimental techniques for testing dynamically substructured systems are currently receiving attention in a wide range of structural, aerospace and automotive engineering environments. Dynamic substructuring enables full‐size, critical components to be physically tested within a laboratory (as physical substructures), while the remaining parts are simulated in real‐time (as numerical substructures). High quality control is required to achieve synchronization of variables at the substructuring interfaces and to compensate for additional actuator system(s) dynamics, nonlinearities, uncertainties and time‐varying parameters within the physical substructures. This paper presents the substructuring approach and associated controller designs for performance testing of an aseismic, base‐isolation system, which is comprised of roller‐pendulum isolators and controllable, nonlinear magnetorheological dampers. Roller‐pendulum isolators are typically mounted between the protected structure and its foundation and have a fundamental period of oscillation far‐removed from the predominant periods of any earthquake. Such semi‐active damper systems can ensure safety and performance requirements, whereas the implementation of purely active systems can be problematic in this respect. A linear inverse dynamics compensation and an adaptive controller are tailored for the resulting nonlinear synchronization problem. Implementation results favourably compare the effectiveness of the adaptive substructuring method against a conventional shaking‐table technique. A 1.32% error resulted compared with the shaking‐table response. Ultimately, the accuracy of the substructuring method compared with the response of the shaking‐table is dependent upon the fidelity of the numerical substructure. Copyright © 2009 John Wiley & Sons, Ltd.

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

AbstractA 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.

실시간 하이브리드 진동대 실험법에 의한 양방향 TLMD의 진동제어 성능평가

An experimental real-time hybrid method, which implements the vibration control of a building structure with only a two-way TLMD, is proposed and verified through a shaking table test. The building structure is divided into the upper experimental TLMD and the lower numerical structural part. The shaking table vibrates the TLMD with the response calculated from the numerical substructure, which is subjected to the excitations of the measured interface control force at its top story and sinusoidal waves input at its base. The results show that the conventional method can be replaced by the proposed methodology with a simple installation and accuracy for evaluating the control performance of a TLMD.

Evaluation of numerical time‐integration schemes for real‐time hybrid testing

AbstractWe present a comparison of methods for the analysis of the numerical substructure in a real‐time hybrid test. A multi‐tasking strategy is described, which satisfies the various control and numerical requirements. Within this strategy a variety of explicit and implicit time‐integration algorithms have been evaluated. Fully implicit schemes can be used in fast hybrid testing via a digital sub‐step feedback technique, but it is shown that this approach requires a large amount of computation at each sub‐step, making real‐time execution difficult for all but the simplest models. In cases where the numerical substructure poses no harsh stability condition, it is shown that the Newmark explicit method offers advantages of speed and accuracy. Where the stability limit of an explicit method cannot be met, one of the several alternatives may be used, such as Chang's modified Newmark scheme or the α‐operator splitting method. Appropriate methods of actuator delay compensation are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.

Hybrid Seismic Response Simulation on a Geographically Distributed Bridge Model

The hybrid simulation test method is a versatile technique for evaluating the seismic performance of structures by seamlessly integrating both physical and numerical simulations of substructures into a single test model. Using hybrid simulation, the seismic response of complex structural systems partitioned into multiple large-scale experimental and numerical substructures at networked geographically distributed experimental and computational facilities can be evaluated. A scalable framework with a fault-tolerant distributed controller is presented to support the implementation of advanced hybrid testing methods with distributed substructures. The control strategy is based on a multithreaded simulation coordinator for parallel communication with remote sites and an event-driven controller at each remote experimental site to implement continuous loading. The distributed controller provides faster rates of testing and improved accuracy in the simulation results. The effectiveness of the proposed framework is demonstrated by computing the earthquake response of a six-span bridge model with multiple remote experimental and numerical column substructures distributed within NEES laboratories across the United States. Further, the distributed tests were implemented using a secure network link between the testing sites that was developed for the NEES cyber infrastructure.

Three More Fish Stories (John 21:11)

(ProQuest: ... denotes formulae omitted.) The perennially interesting conundrum of the 153 fish finds its most complete recent treatment in the commentary of Craig Keener.1 Of the approximately dozen suggestions that are highlighted there, it is probably fair to say that the one holding sway at this moment sees the number as gematrical sum alluding to the Hebrew for children of God. In this critical note, I wish to add three suggestions to the hopper. 1. Peter when old. This is perhaps the simplest of the three suggestions, based on an inter-Greek exercise of gematria. The number 153 is the sum of the digits of the following Greek letters: gamma, rho, nu. γ = 3 ρ = 100 v = 50 These letters form the consonantal spine of the word for old, in verbal form applied by Jesus to Peter in John 21:18.2 2. Justice. As described by the neo-Pythagorean Iamblichus, justice is a power of rendering what is equal and fitting comprehended by the of an odd square number.3 This fourth-century C.E. definition, preserving earlier tradition, is relevant to the Fourth Gospel in the following way: The first odd number is 3; its square is 9.4 The of 9 is 5. Five is the mean of the number of fish 1, 5, 3. There are also five places in the farewell discourse, each buffered by different theme, where the disciples are commanded to ask (...).5 Further, according to one recent commentator, five provides the numerical substructure of the whole text.6 By his having returned to the Father, Jesus has demonstrated the justice of God (16:10), and that justice is here adumbrated in the 153 fish. 3. Providence. The sum of the digits in 153 is 9,7 and it occurs following portion of the text in which eight people are present at the cross of Jesus.8 This 8, 9 sequence is used as structuring principle in Sirach's panegyric in honor of Simeon the high priest, according to recent article by Jeremy Corley.9 He links this pattern to statements in Sir 18:6 and 42:21 and Qoh 3:14 and suggests that the numerical pattern alludes to the exact providence of God's action in history, where nothing needs to be added and nothing subtracted.10 John's attention to 8 and 9 may have similar intention of praising God's providence in the history of its preeminent high priest, Jesus. Moreover, the sum of 8 and 9 is 17,11 and 153 is the result of multiplying 9 × 17. This increase and multiply dynamic may be playing with Gen 1:28 LXX, whose ... is directed to the man and woman. The double command echoes the identical command to the sea creatures in Gen 1:22, though 1:28 goes on to give the couple dominion over the fish of the sea. Therefore, the providential reading of 153 is grounded in the lifting up of Jesus as well as in the initial creative and sustaining will of God. Conclusion. Each of these three options presents itself against horizon-ofnine. Nine is present in option 2's square of 3, as well as in the sum of the digits and use of 9 as multiple in option 3. Nine is remote horizon for option 1 as well: The high point of Peter's confession, that which acts as immediate pretext for the Peter-as-old saying, contains nine words in the Greek: ..., , Lord, know everything, know that I love you (21:17). We cannot be certain about the evangelist's motivation in utilizing 9 as background horizon. Perhaps the fact that the last items in the Hebrew lexicon build on the nine stem, JJWn, suggested the root as fitting one for the conclusion of the text. We know, after all, that Daniel's 1,290 days (Dan 12:11) constitute the penultimate statement ofthat apocalyptic presentation. The Johannine editor may have chosen this numerical frame as suitable one for the text's final reflection on Jesus' coming (21:23). …

Numerical simulation of dynamic soil–structure interaction in shaking table testing

This paper provides an insight into the numerical simulation of soil–structure interaction (SSI) phenomena studied in a shaking table facility. The shaking table test is purposely designed to confirm the ability of the numerical substructure technique to simulate the SSI phenomenon. A model foundation–structure system with strong SSI potential is embedded in a dry bed of sand deposited within a purpose designed shaking-table soil container. The experimental system is subjected to a strong ground motion. The numerical simulation of the complete soil–foundation–structure system is conducted in the linear viscoelastic domain using the substructure approach. The matching of the experimental and numerical responses in both frequency and in time domain is satisfying. Many important aspects of SSI that are apparent in the experiment are captured by the numerical simulation. Furthermore, the numerical modelling is shown to be adequate for practical engineering design purposes.

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

AbstractThe 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.

Compensation of actuator dynamics in real-time hybrid tests

Real-time hybrid testing is a novel approach to the dynamic testing of structures, in which the system under test is split into physical and numerical substructures which are tested and analysed in parallel, with data passed between them in real time. The success of a test is highly dependent on the performance of the actuators which provide the interface forces and displacements between the two substructures. This paper presents several numerical schemes to compensate for the non-ideal dynamics of typical servohydraulic actuators and evaluates them through a series of real-time hybrid tests on simple mass-spring systems. It is shown that effective schemes can be developed on the basis of a simple representation of the actuator response as combination of a delay and an amplitude error, both of which can vary during a test. The use of a modified online delay estimator, together with one of three simple forward extrapolation schemes, is found to be highly effective in minimizing experimental errors related to the actuator dynamics.

Real-time substructuring technique for the shaking table test of upper substructures

In this study, a real-time substructuring technique for the shaking table test is proposed. The proposed technique adopts the upper part of the object structure as the experimental substructure and the lower part as the numerical substructure. The force exerted on the interface of the two separated substructures is calculated on-line using the feed-back from an absolute floor acceleration measurement. The acceleration at the interface of the two substructures is calculated through an on-line time history analysis of the numerical substructure and is used as a reference signal in the shaking table controller. The inverse transfer function of the shaking table is employed to minimize the errors between the reference signal and generated ground motion for the experimental substructure. Through a shaking table test, the validity and accuracy of the proposed technique is demonstrated, and a good agreement between experimental and numerical results is obtained.

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

AbstractReal‐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.

Architecture, Caching, and Foreign Contacts at Chac (II), Yucatan, Mexico

AbstractThe Puuc region of northern Yucatan was one of the most important areas of Maya civilization during the Terminal Classic florescent period. Despite its importance to Maya prehistory, there is little understanding of the times prior to the great cultural florescence. Eight seasons of research at Chac II provide new information regarding an important Maya center between the Classic and Terminal Classic periods (A.D. 300–800), including the changing nature of influence and contacts with foreign groups reaching central Mexico. The great antiquity of Chac, the presence of numerous substructures, and the variety of architectural styles in the Great Pyramid Plaza suggest that the site was an originator of the Early Puuc architectural style. It is argued that the major ritual offering below the central monument at the Gran Plaza re-creates the “turquoise” hearth reenacting the birth of the Fifth Sun at Teotihuacan. These new data are transforming understanding of the Puuc Maya and their relations with greater Mesoamerica.

Event-Driven Control System for Geographically Distributed Hybrid Simulation

An event-driven distributed control system for conducting continuous seismic response simulations using geographically distributed hybrid models is presented. Hybrid models, comprising appropriately scaled experimental and numerical substructures in networked geographically distributed laboratories or computers, can be used to realistically and cost-effectively evaluate the performance of complex structures at large scales. The principal advantage of the proposed event-driven control system is its ability to mitigate the adverse effects of random completion times of communication, computation, actuation and measurement tasks during a hybrid simulation on the stability, accuracy and reliability of the simulation results. The efficiency of the proposed continuous extrapolation/interpolation hybrid simulation method is demonstrated by examining the earthquake response of a two-story shear building model that comprises two experimental substructures and a numerical integrator connected through the internet. An evaluation of results from these hybrid simulations suggests that distributed hybrid simulation conducted using the proposed procedure provides accurate and reliable results.

On-line hybrid test combining with general-purpose finite element software

A new on-line hybrid test system incorporated with the substructuring technique is developed. In this system, a general-purpose finite element software is employed to obtain the restoring forces of the numerical substructure accurately. The restart option is repeatedly used to accommodate the software with alternating loading and analysis characteristic of the on-line test but without touching the source code. An eight-storey base-isolated structure is tested to evaluate the feasibility and effectiveness of the proposed test system. The overall structure is divided into two substructures, i.e. a superstructure to be analysed by the software and a base-isolation layer to be tested physically. Collisions between the base-isolation layer and the surrounding walls are considered in the test. The responses of the overall structure are reasonable, and smooth operation is achieved without any malfunction. Copyright © 2006 John Wiley & Sons, Ltd.

Bond-graph based substructuring of dynamical systems

A bond graph approach to hybrid simulation of dynamical systems using numerical–experimental real-time substructuring is presented. The bond graph concepts of a virtual junction and a virtual actuator, hitherto used in the context of physical-model based control, are used to perform the substructuring in an intuitively appealing way. The approach is illustrated by the reworking of a previously-published example. The approach is verified experimentally using a bench-top multiple mass–spring system for the physical substructure and automatically generated real-time code is used to implement the numerical substructure. 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 ...

Pseudodynamic tests on rubber base isolators with numerical substructuring of the superstructure and strain‐rate effect compensation

AbstractA pseudodynamic testing procedure has been applied by which the seismic response of a base‐isolated building is obtained by using as specimen the isolators, while the superstructure is numerically simulated. The procedure also takes advantage of the continuous pseudodynamic testing capabilities of the ELSA laboratory, which increase the accuracy of the results and reduce the strain‐rate effect of the rubber bearings. A simple proportional correction of the measured forces compensates the remaining strain‐rate effect due to the unrealistic speed of the test. The correction factor is obtained by means of a characterizing test on the specific rubber isolators.The developed method has been successfully applied to the prediction of the seismic response of a base‐isolated four‐storey building submitted to several specified accelerograms. The results for those earthquakes as well as the effects of some changes of the parameters of the system are discussed. Copyright © 2002 John Wiley & Sons, Ltd.

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.