A simple strategy for dynamic substructuring: I. Concept and development

Dynamic substructuring refers to physical testing with computational models in the loop. This paper presents a new strategy for such testing. The key feature of this strategy is that it decouples the substructuring controller from the physical subsystem. Unlike conventional approaches, it does not explicitly include a tracking controller. Consequently, the design and implementation of the substructuring controls are greatly simplified. This paper motivates the strategy and discusses the main concept along with details of the substructuring control design. The focus is on configurations that use shake tables and active mass drivers. An extensive experimental assessment of the new strategy is presented in a companion paper, where the influence of various factors such as virtual subsystem dynamics, control gains, and nonlinearities is investigated, and it is shown that robustly stable and accurate substructuring is achieved.     

Pseudo‐dynamic testing with substructuring at the ELSA Laboratory

The paper describes the distinctive features of the pseudo‐dynamic test method as implemented at the ELSA reaction‐wall facility. Both hardware and software aspects are considered. Particular attention is devoted to the digital control system and to a coupled numerical–experimental substructuring technique allowing realistic earthquake testing of very large structures. Mathematical and implementation details corresponding to this testing technique are given for both synchronous and asynchronous input motion. Selected test results illustrate the advantages of the presented features. Copyright © 2000 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.     

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.     

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

Experimental 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.     

Comparison between real‐time dynamic substructuring and shake table testing techniques for nonlinear seismic applications

Results from real‐time dynamic substructuring (RTDS) tests are compared with results from shake table tests performed on a two‐storey steel building structure model. At each storey, the structural system consists of a cantilevered steel column resisting lateral loads in bending. In two tests, a slender diagonal tension‐only steel bracing member was added at the first floor to obtain an unsymmetrical system with highly variable stiffness. Only the first‐storey structural components were included in the RTDS test program and a Rosenbrock‐W linearly implicit integration scheme was adopted for the numerical solution. The tests were performed under seismic ground motions exhibiting various amplitude levels and frequency contents to develop first and second mode‐dominated responses as well as elastic and inelastic responses. A chirp signal was also used. Coherent results were obtained between the shake table and the RTDS testing techniques, indicating that RTDS testing methods can be used to successfully reproduce both the linear and nonlinear seismic responses of ductile structural steel seismic force resisting systems. The time delay introduced by actuator‐control systems was also studied and a novel adaptive compensation scheme is proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

A computational workflow for rupture‐to‐structural‐response simulation and its application to Istanbul

Scenario‐based earthquake simulations at regional scales hold the promise in advancing the state‐of‐the‐art in seismic risk assessment studies. In this study, a computational workflow is presented that combines (i) a broadband Green's function‐based fault‐rupture and ground motion simulation—herein carried out using the “UCSB (University of California at Santa Barbara) method”, (ii) a three‐dimensional physics‐based regional‐scale wave propagation simulation that is resolved at  Hz, and (iii) a local soil‐foundation‐structure finite element analysis model. These models are interfaced with each other using the domain reduction method. The innermost local model—implemented in ABAQUS—is additionally enveloped with perfectly matched layer boundaries that absorb outbound waves scattered by the structures contained within it. The intermediate wave propagation simulation is carried out using Hercules , which is an explicit time‐stepping finite element code that is developed and licensed by the CMU‐QUAKE group. The devised workflow is applied to a  km region on the European side of Istanbul, which was modeled using detailed soil stratigraphy data and realistic fault rupture properties, which are available from prior microzonation surveys and earthquake scenario studies. The innermost local model comprises a chevron‐braced steel frame building supported by a shallow foundation slab, which, in turn, rests atop a three‐dimensional soil domain. To demonstrate the utility of the workflow, results obtained using various simplified soil‐structure interaction analysis techniques are compared with those from the detailed direct model. While the aforementioned demonstration has a limited scope, the devised workflow can be used in a multitude of ways, for example, to examine the effects of shallow‐layer soil nonlinearities and surface topography, to devise site‐ and structure‐specific seismic fragilities, and for calibrating regional loss models, to name a few.     

Control issues relating to real‐time substructuring experiments using a shaking table

Real‐time substructuring is a method of dynamically testing a structure without experimentally testing a physical model of the entire system. Instead the structure can be split into two linked parts, the region of particular interest, which is tested experimentally, and the remainder which is tested numerically. A transfer system, such as a hydraulic actuator or a shaking table, is used to impose the displacements at the interface between the two parts on the experimental substructure. The corresponding force imposed by the substructure on the transfer system is fed back to the numerical model. Control of the transfer system is critical to the accuracy of the substructuring process. A study of two controllers used in conjunction with the University of Bristol shaking table is presented here. A proof‐of‐concept one degree‐of‐freedom mass–spring–damper system is substructured such that a portion of the mass forms the experimental substructure and the remainder of the mass plus the spring and the damper is modelled numerically. Firstly a linear controller is designed and tested. Following this an adaptive substructuring strategy is considered, based on the minimal control synthesis algorithm. The deleterious effect of oil‐column resonance common to shaking tables is examined and reduced through the use of filters. The controlled response of the experimental specimen is compared for the two control strategies. Copyright © 2005 John Wiley & Sons, Ltd.     

Stability analysis of real‐time dynamic substructuring using delay differential equation models

Real‐time dynamic substructuring is an experimental technique for testing the dynamic behaviour of complex structures. It involves creating a hybrid model of the entire structure by combining an experimental test piece—the substructure—with a numerical model describing the remainder of the system. The technique is useful when it is impractical to experimentally test the entire structure or complete numerical modelling is insufficient. In this paper, we focus on the influence of delay in the system, which is generally due to the inherent dynamics of the transfer systems (actuators) used for structural testing. This naturally gives rise to a delay differential equation (DDE) model of the substructured system. With the case of a substructured system consisting of a single mass–spring oscillator we demonstrate how a DDE model can be used to understand the influence of the response delay of the actuator. Specifically, we describe a number of methods for identifying the critical time delay above which the system becomes unstable. Because of the low damping in many large structures a typical situation is that a substructuring test would operate in an unstable region if additional techniques were not implemented in practice. We demonstrate with an adaptive delay compensation technique that the substructured mass–spring oscillator system can be stabilized successfully in an experiment. The approach of DDE modelling also allows us to determine the dependence of the critical delay on the parameters of the delay compensation scheme. Using this approach we develop an over‐compensation scheme that will help ensure stable experimental testing from initiation to steady state operation. This technique is particularly suited to stiff structures or those with very low natural damping as regularly encountered in structural engineering. Copyright © 2005 John Wiley & Sons, Ltd.     

Influence of free field variability on linear soil–structure interaction (SSI) by indirect integral representation

An integral equation for the representation of the response of a structure impinged by an incident wave field including soil–structure interaction is proposed. It requires the knowledge of the fundamental solution for the overall soil–structure domain when a unit load is applied to the structure. This fundamental solution is obtained by means of a substructuring technique and boundary integral equations using the Green tensors for homogeneous or horizontally stratified soil media. The effects of a non‐stationary modulated random incident field are addressed in terms of the instantaneous power spectral density of the structural response of interest for a given coherency function of the free field. Several applications of the proposed procedure are presented. The first one considers kinematic interaction of a rigid circular foundation and is used to validate the numerical implementation. The second one considers a complex structure on a stiff stratified soil and the last one considers the pounding effect between two adjacent, identical structures resting on a thin soft soil layer. Copyright © 2002 John Wiley & Sons, Ltd.